2000 AMC 8 Problems/Problem 10

Problem

Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?

$\text{(A)}\ 48 \qquad \text{(B)}\ 51 \qquad \text{(C)}\ 52 \qquad \text{(D)}\ 54 \qquad \text{(E)}\ 55$

Solution

Shea has grown $20\%$ , if x was her original height, then $1.2x = 60$ , so she was originally $\frac{60}{1.2}=50$ inches tall which is a $60 - 50 = 10$ inch increase. Ara also started off at $50$ inches. Since Ara grew half as much as Shea, Ara grew $\frac{10}{2} = 5$ inches. Therefore, Ara is now $50+5=55$ inches tall which is choice $\boxed{E}.$

2000 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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2000 AMC 8 Problems/Problem 10

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