# 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 $\fbox{B}$.

## Solution 2

Using average, we know that assuming the middle-aged people's ticket cost x dollars, 2*(100%x+75%x+50%x). We average this into 2*(75%x+75%x+75%x). We know that 75%x=6.00, which means 6*6 is the answer, or 36. -RealityWrites

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