2009 AMC 10A Problems/Problem 8

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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?

$\mathrm{(A)}\ 34\qquad\mathrm{(B)}\ 36\qquad\mathrm{(C)}\ 42\qquad\mathrm{(D)}\ 46\qquad\mathrm{(E)}\ 48$

Solution

A senior ticket costs $ $6.00$ , so a regular ticket costs $6 \cdot \frac{1}{\frac{3}{4}}\:=\:6\cdot\frac{4}{3}\:=\:8$ dollars. Therefore children's tickets cost half that, or $ $4.00$ , so we have:

$2(6+8+4)\:=\:36$

So Grandfather Wen pays $ $36$ , or $B$ .

2009 AMC 10A (Problems • Resources)
Preceded by Problem 7	Followed by Problem 9
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2009 AMC 10A Problems/Problem 8

From AoPSWiki

Problem 8

Solution

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