AMC 8 2000 Problem 10

AMC8 2000 年第 10 题

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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?

Ara 和 Shea 以前身高一样。自那以后，Shea 身高增高了 20％，而 Ara 增长的高度是 Shea 增长高度的一半。Shea 现在身高 60 英寸，那么 Ara 现在身高是多少英寸？

A.48
B.51
C.52
D.54
E.55

正确答案 · Correct Answer

解析 · Solution

Solution 1

Shea has grown 20%, if x was her original height, then 1.2x = 60, so she was originally

\displaystyle \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

\displaystyle \frac{10}{2} = 5

inches. Therefore, Ara is now 50+5=55 inches tall which is choice $E.$

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