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Difference between revisions of "2009 AMC 10A Problems"

(→‎Problem 7)
(→‎Problem 8)
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== Problem 8 ==
 
== Problem 8 ==
 +
Three Generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a <math>50</math>% discount as children. The two members of the oldest generation receive a <math>25</math>% discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs <math>6.00, is paying for everyone. How many dollars must he pay?
 +
 +
</math>a)\, 34\qquad
 +
b)\, 36\qquad
 +
c)\, 42\qquad
 +
d)\, 46\qquad
 +
e)\, 48$
  
 
[[2009 AMC 10A Problems/Problem 8|Solution]]
 
[[2009 AMC 10A Problems/Problem 8|Solution]]

Revision as of 21:31, 11 February 2009

Problem 1

One can holds $12$ ounces of soda. What is the minimum number of cans needed to provide a gallon (128 ounces) of soda? $a)\, 7\qquad b)\, 8\qquad c)\, 9\qquad d)\, 10\qquad e)\, 11$

Solution

Problem 2

Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes and quarters. Which of the following could not be the total value of the four coins, in cents?

$a)\, 15\qquad b)\, 25\qquad c)\, 35\qquad d)\, 45\qquad e)\, 55$

Solution

Problem 3

Which of the following is equal to $1 + \frac{1}{1+\frac{1}{1+1}}$?

$a)\, \frac{5}{4}\qquad b)\, \frac{3}{2}\qquad c)\, \frac{5}{3}\qquad d)\, 2\qquad e)\, 3$

Solution

Problem 4

Eric plans to compete in a triathalon. He can average $2$ miles per hour in the $\frac{1}{4}$-mile swim and $6$ miles per hour in the $3$-mile run. His goal is to finish the triathlon in $2$ hours. To accomplish his goal what must his average speed in miles per hour, be for the $15$-mile bicycle ride?

$a)\, \frac{120}{11}\qquad b)\, 11\qquad c)\, \frac{56}{5}\qquad d)\, \frac{45}{4}\qquad e)\, 12$

Solution

Problem 5

What is the sum of the digits of the square of $111,111,111$?

$a)\, 18\qquad b)\, 27\qquad c)\, 45\qquad d)\, 63\qquad e)\, 81$

Solution

Problem 6

Solution

Problem 7

A carton contains milk that is $2$% fat, an amount that is $40$% less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?

$a)\, \frac{12}{5}\qquad b)\, \frac{10}{3}\qquad c)\, 9\qquad d)\, 38\qquad e)\, 42$

Solution

Problem 8

Three Generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a $50$% discount as children. The two members of the oldest generation receive a $25$% discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs $6.00, is paying for everyone. How many dollars must he pay?$a)\, 34\qquad b)\, 36\qquad c)\, 42\qquad d)\, 46\qquad e)\, 48$

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

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