Difference between revisions of "1997 PMWC Problems/Problem I6"

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== Problem ==
 
== Problem ==
John and Mary went to a book shop and bought some exercise books. They had <math>\</math>100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had <math>\</math>5 left. How much was a small exercise book?
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John and Mary went to a book shop and bought some exercise books. They had <math>\textdollar 100</math> each. John could buy <math>7</math> large and <math>4</math> small ones. Mary could buy <math>5</math> large and <math>6</math> small ones and had <math>\textdollar 5</math> left. How much was a small exercise book?
 
  
 
== Solution ==
 
== Solution ==
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Plugging them back in, we see that they work.
 
Plugging them back in, we see that they work.
  
== See also ==
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== See Also ==
 
{{PMWC box|year=1997|num-b=I5|num-a=I7}}
 
{{PMWC box|year=1997|num-b=I5|num-a=I7}}
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Latest revision as of 13:23, 20 April 2014

Problem

John and Mary went to a book shop and bought some exercise books. They had $\textdollar 100$ each. John could buy $7$ large and $4$ small ones. Mary could buy $5$ large and $6$ small ones and had $\textdollar 5$ left. How much was a small exercise book?

Solution

$7l+4s=100$

$5l+6s=95$

$2l-2s=5$

$6s-6l=-15$

$11l=110$

$l=10$

$s=\dfrac{15}{2}$

Plugging them back in, we see that they work.

See Also

1997 PMWC (Problems)
Preceded by
Problem I5
Followed by
Problem I7
I: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T: 1 2 3 4 5 6 7 8 9 10