AMC12 2006 A

AMC12 2006 A · Q7

AMC12 2006 A · Q7. It mainly tests Linear equations, Percent.

Mary is $20\%$ older than Sally, and Sally is $40\%$ younger than Danielle. The sum of their ages is $23.2$ years. How old will Mary be on her next birthday?

Mary 比 Sally 大 $20\%$，而 Sally 比 Danielle 小 $40\%$。她们年龄之和为 $23.2$ 岁。Mary 下一个生日时多大？

(A) 7 7

(B) 8 8

(D) 10 10

(E) 11 11

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $m$ be Mary's age, let $s$ be Sally's age, and let $d$ be Danielle's age. We have $s=.6d$, and $m=1.2s=1.2(.6d)=.72d$. The sum of their ages is $m+s+d=.72d+.6d+d=2.32d$. Therefore, $2.32d=23.2$, and $d=10$. Then $m=.72(10)=7.2$. Mary will be $8$ on her next birthday. The answer is $\mathrm{(B)}$.

设 Mary 的年龄为 $m$，Sally 的年龄为 $s$，Danielle 的年龄为 $d$。有 $s=.6d$，且 $m=1.2s=1.2(.6d)=.72d$。她们年龄之和为 $m+s+d=.72d+.6d+d=2.32d$。因此 $2.32d=23.2$，得 $d=10$。于是 $m=.72(10)=7.2$。Mary 下一个生日时将是 $8$ 岁。答案是 $\mathrm{(B)}$。

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