https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Danb80&feedformat=atomAoPS Wiki - User contributions [en]2021-10-16T23:52:05ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=File:Table.gif&diff=17780File:Table.gif2007-10-10T14:10:05Z<p>Danb80: </p>
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<div></div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I15&diff=176701997 PMWC Problems/Problem I152007-10-08T21:47:33Z<p>Danb80: New page: 26</p>
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<div>26</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176691997 PMWC2007-10-08T21:47:18Z<p>Danb80: /* Problem I15 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
[[Image:ABCD.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
In a die, 1 and 6,2 and 5,3 and 4 appear on opposite faces.<br />
When 2 dice are thrown, product of numbers appearing on<br />
the top and bottom faces of the 2 dice are formed as follows:<br />
number on top face of 1 st die x number on top face of 2nd die<br />
number on top face of 1st die x number on bottom face of 2nd die<br />
number on bottom face of 1st die x number on top face of 2nd die<br />
number on bottom face of 1st die x number on bottom face of 2nd die<br />
What is the sum of these 4 products ?<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
A truck moved from A to B at a speed of 50 km/h and<br />
returns fi-om B to A at 70 km/h. It traveled 3 rounds within<br />
18 hours. What is the distance between A and B?<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
If we make five two-digit numbers using the digits 0, 1, 2,...9 exactly once, and the product of the five numbers is maximized, find the greatest number among them.<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
How many paths from A to B consist of exactly six line<br />
segments (vertical, horizontal or inclined)?<br />
[[Image:AB.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176681997 PMWC2007-10-08T21:46:54Z<p>Danb80: /* Problem I15 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
[[Image:ABCD.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
In a die, 1 and 6,2 and 5,3 and 4 appear on opposite faces.<br />
When 2 dice are thrown, product of numbers appearing on<br />
the top and bottom faces of the 2 dice are formed as follows:<br />
number on top face of 1 st die x number on top face of 2nd die<br />
number on top face of 1st die x number on bottom face of 2nd die<br />
number on bottom face of 1st die x number on top face of 2nd die<br />
number on bottom face of 1st die x number on bottom face of 2nd die<br />
What is the sum of these 4 products ?<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
A truck moved from A to B at a speed of 50 km/h and<br />
returns fi-om B to A at 70 km/h. It traveled 3 rounds within<br />
18 hours. What is the distance between A and B?<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
If we make five two-digit numbers using the digits 0, 1, 2,...9 exactly once, and the product of the five numbers is maximized, find the greatest number among them.<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
How many paths from A to B consist of exactly six line<br />
segments (vertical, horizontal or inclined)?<br />
[[Image:AB,gif]]<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=File:AB.gif&diff=17667File:AB.gif2007-10-08T21:46:27Z<p>Danb80: </p>
<hr />
<div></div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I14&diff=176661997 PMWC Problems/Problem I142007-10-08T21:44:35Z<p>Danb80: New page: 90</p>
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<div>90</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176651997 PMWC2007-10-08T21:44:16Z<p>Danb80: /* Problem I14 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
[[Image:ABCD.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
In a die, 1 and 6,2 and 5,3 and 4 appear on opposite faces.<br />
When 2 dice are thrown, product of numbers appearing on<br />
the top and bottom faces of the 2 dice are formed as follows:<br />
number on top face of 1 st die x number on top face of 2nd die<br />
number on top face of 1st die x number on bottom face of 2nd die<br />
number on bottom face of 1st die x number on top face of 2nd die<br />
number on bottom face of 1st die x number on bottom face of 2nd die<br />
What is the sum of these 4 products ?<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
A truck moved from A to B at a speed of 50 km/h and<br />
returns fi-om B to A at 70 km/h. It traveled 3 rounds within<br />
18 hours. What is the distance between A and B?<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
If we make five two-digit numbers using the digits 0, 1, 2,...9 exactly once, and the product of the five numbers is maximized, find the greatest number among them.<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176631997 PMWC2007-10-08T21:42:56Z<p>Danb80: /* Problem I13 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
[[Image:ABCD.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
In a die, 1 and 6,2 and 5,3 and 4 appear on opposite faces.<br />
When 2 dice are thrown, product of numbers appearing on<br />
the top and bottom faces of the 2 dice are formed as follows:<br />
number on top face of 1 st die x number on top face of 2nd die<br />
number on top face of 1st die x number on bottom face of 2nd die<br />
number on bottom face of 1st die x number on top face of 2nd die<br />
number on bottom face of 1st die x number on bottom face of 2nd die<br />
What is the sum of these 4 products ?<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
A truck moved from A to B at a speed of 50 km/h and<br />
returns fi-om B to A at 70 km/h. It traveled 3 rounds within<br />
18 hours. What is the distance between A and B?<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I12&diff=176621997 PMWC Problems/Problem I122007-10-08T21:41:50Z<p>Danb80: New page: 49</p>
<hr />
<div>49</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176611997 PMWC2007-10-08T21:41:30Z<p>Danb80: /* Problem I12 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
[[Image:ABCD.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
In a die, 1 and 6,2 and 5,3 and 4 appear on opposite faces.<br />
When 2 dice are thrown, product of numbers appearing on<br />
the top and bottom faces of the 2 dice are formed as follows:<br />
number on top face of 1 st die x number on top face of 2nd die<br />
number on top face of 1st die x number on bottom face of 2nd die<br />
number on bottom face of 1st die x number on top face of 2nd die<br />
number on bottom face of 1st die x number on bottom face of 2nd die<br />
What is the sum of these 4 products ?<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I11&diff=176601997 PMWC Problems/Problem I112007-10-08T21:40:14Z<p>Danb80: New page: 330 cm.</p>
<hr />
<div>330 cm.</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176591997 PMWC2007-10-08T21:39:41Z<p>Danb80: /* Problem I11 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
[[Image:ABCD.gif]]<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=File:ABCD.gif&diff=17658File:ABCD.gif2007-10-08T21:39:03Z<p>Danb80: </p>
<hr />
<div></div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176571997 PMWC2007-10-08T21:36:09Z<p>Danb80: /* Problem I11 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>. <br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176561997 PMWC2007-10-08T21:35:32Z<p>Danb80: /* Problem I11 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is 6750 cm<math>^2</math>. <br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176551997 PMWC2007-10-08T21:35:08Z<p>Danb80: /* Problem I11 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is 6750 <math>/cm^2</math>. <br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I10&diff=176541997 PMWC Problems/Problem I102007-10-08T21:29:03Z<p>Danb80: New page: 6</p>
<hr />
<div>6</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I9&diff=176531997 PMWC Problems/Problem I92007-10-08T21:28:02Z<p>Danb80: New page: 7500</p>
<hr />
<div>7500</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176511997 PMWC2007-10-08T21:27:12Z<p>Danb80: /* Problem I9 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176501997 PMWC2007-10-08T21:26:51Z<p>Danb80: /* Problem T9 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I7&diff=176491997 PMWC Problems/Problem I72007-10-08T21:26:14Z<p>Danb80: New page: 27</p>
<hr />
<div>27</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176471997 PMWC2007-10-08T21:25:25Z<p>Danb80: /* Problem I7 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176461997 PMWC2007-10-08T21:25:03Z<p>Danb80: /* Problem T7 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I6&diff=176451997 PMWC Problems/Problem I62007-10-08T21:24:32Z<p>Danb80: New page: <dollar/>7.50</p>
<hr />
<div><dollar/>7.50</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176431997 PMWC2007-10-08T21:23:54Z<p>Danb80: /* Problem I6 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176421997 PMWC2007-10-08T21:23:27Z<p>Danb80: /* Problem T6 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_T3&diff=176411997 PMWC Problems/Problem T32007-10-08T21:22:49Z<p>Danb80: Removing all content from page</p>
<hr />
<div></div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I3&diff=176401997 PMWC Problems/Problem I32007-10-08T21:21:50Z<p>Danb80: New page: 11 p.m. Wednesday</p>
<hr />
<div>11 p.m. Wednesday</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176391997 PMWC2007-10-08T21:20:54Z<p>Danb80: /* Problem I3 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when will he take them altogether again?<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176381997 PMWC2007-10-08T21:20:19Z<p>Danb80: /* Problem T3 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176371997 PMWC2007-10-08T21:19:45Z<p>Danb80: /* Problem I10 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
Mary took 24 chickens to the market. In the morning she<br />
sold the chickens at <math>7 each and she only sold out less than<br />
half of them. In the afternoon she discounted the price of<br />
each chicken but the price was still an integral number in<br />
dollar. In the afternoon she could sell all the chickens, and<br />
she got totally </math>132 for the whole day. How many<br />
chickens were sold in the morning?<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176351997 PMWC2007-10-08T21:17:37Z<p>Danb80: /* Problem T9 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
A chemist mixed an acid of 48% concentration with the<br />
same acid of 80% concentration, and then added 2 litres of<br />
distilled water to the mixed acid. As a result, he got 10<br />
litres of the acid of 40% concentration. How many<br />
millilitre of the acid of 48% concentration that the chemist<br />
had used? (1 litre = 1000 millilitres)<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176331997 PMWC2007-10-08T21:15:44Z<p>Danb80: /* Problem T7 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
40% of girls and 50% of boys in a class got 'A'. If there<br />
are only 12 students in the class got 'A's and the ratio of<br />
boys and girls in the class is 45, how many students are<br />
there in the class?<br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176301997 PMWC2007-10-08T21:13:44Z<p>Danb80: /* Problem T6 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176291997 PMWC2007-10-08T21:13:09Z<p>Danb80: /* Problem T6 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some exercise books. They had <dollar/><math>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <dollar/></math>5 left. How much was a small exercise book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176281997 PMWC2007-10-08T21:11:53Z<p>Danb80: /* Problem T6 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
John and Mary went to a book shop and bought some<br />
exercise books. They had <math>100 each. John could buy 7<br />
large and 4 small ones. Mary could buy 5 large and 6 small<br />
ones and had </math>5 left. How much was a small exercise<br />
book?<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_T3&diff=176271997 PMWC Problems/Problem T32007-10-08T21:10:38Z<p>Danb80: New page: 11 p.m. Wednesday</p>
<hr />
<div>11 p.m. Wednesday</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176261997 PMWC2007-10-08T21:10:14Z<p>Danb80: /* Problem T3 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
Peter is ill. He has to take medicine A every 8 hours,<br />
medicine B every 5 hours and medicine C every 10 hours.<br />
If he took all three medicines at 7 a.m. on Tuesday, when<br />
will he take them altogether again?<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176251997 PMWC2007-10-08T21:09:22Z<p>Danb80: /* Problem I2 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176241997 PMWC2007-10-08T21:08:51Z<p>Danb80: /* Problem I2 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
In the multiplication on the right, each letter and each █ represent a single digit. Different letters represent different digits but a █ can represent any digit. What is the five-digit number "HAPPY" stands for?<br />
<br />
█ 1 █<br />
<br />
x 9 █<br />
_________<br />
█ █ 9 █<br />
<br />
█ █ █ 7 █<br />
_________<br />
H A P P Y<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC_Problems/Problem_I1&diff=176231997 PMWC Problems/Problem I12007-10-08T20:55:34Z<p>Danb80: New page: 837 1/420</p>
<hr />
<div>837 1/420</div>Danb80https://artofproblemsolving.com/wiki/index.php?title=1997_PMWC&diff=176221997 PMWC2007-10-08T20:55:11Z<p>Danb80: /* Problem I1 */</p>
<hr />
<div>== Problem I1 ==<br />
Evaluate 29 27/28 x 27 14/15<br />
[[1997 PMWC Problems/Problem I1|Solution]]<br />
<br />
== Problem I2 ==<br />
<br />
[[1997 PMWC Problems/Problem I2|Solution]]<br />
<br />
== Problem I3 ==<br />
<br />
[[1997 PMWC Problems/Problem I3|Solution]]<br />
<br />
== Problem I4 ==<br />
<br />
[[1997 PMWC Problems/Problem I4|Solution]]<br />
<br />
== Problem I5 ==<br />
<br />
[[1997 PMWC Problems/Problem I5|Solution]]<br />
<br />
== Problem I6 ==<br />
<br />
[[1997 PMWC Problems/Problem I6|Solution]]<br />
<br />
== Problem I7 ==<br />
<br />
[[1997 PMWC Problems/Problem I7|Solution]]<br />
<br />
== Problem I8 ==<br />
<br />
[[1997 PMWC Problems/Problem I8|Solution]]<br />
<br />
== Problem I9 ==<br />
<br />
[[1997 PMWC Problems/Problem I9|Solution]]<br />
<br />
== Problem I10 ==<br />
<br />
[[1997 PMWC Problems/Problem I10|Solution]]<br />
<br />
== Problem I11 ==<br />
<br />
[[1997 PMWC Problems/Problem I11|Solution]]<br />
<br />
== Problem I12 ==<br />
<br />
[[1997 PMWC Problems/Problem I12|Solution]]<br />
<br />
== Problem I13 ==<br />
<br />
[[1997 PMWC Problems/Problem I13|Solution]]<br />
<br />
== Problem I14 ==<br />
<br />
[[1997 PMWC Problems/Problem I14|Solution]]<br />
<br />
== Problem I15 ==<br />
<br />
[[1997 PMWC Problems/Problem I15|Solution]]<br />
<br />
== Problem T1 ==<br />
<br />
[[1997 PMWC Problems/Problem T1|Solution]]<br />
<br />
== Problem T2 == <br />
<br />
[[1997 PMWC Problems/Problem T2|Solution]]<br />
<br />
== Problem T3 ==<br />
<br />
[[1997 PMWC Problems/Problem T3|Solution]]<br />
<br />
== Problem T4 == <br />
<br />
[[1997 PMWC Problems/Problem T4|Solution]]<br />
<br />
== Problem T5 ==<br />
<br />
[[1997 PMWC Problems/Problem T5|Solution]]<br />
<br />
== Problem T6 ==<br />
<br />
[[1997 PMWC Problems/Problem T6|Solution]]<br />
<br />
== Problem T7 == <br />
<br />
[[1997 PMWC Problems/Problem T7|Solution]]<br />
<br />
== Problem T8 ==<br />
<br />
[[1997 PMWC Problems/Problem T8|Solution]]<br />
<br />
== Problem T9 ==<br />
<br />
[[1997 PMWC Problems/Problem T9|Solution]]<br />
<br />
== Problem T10 ==<br />
<br />
[[1997 PMWC Problems/Problem T10|Solution]]</div>Danb80