AMC12 2017 B

AMC12 2017 B · Q1

AMC12 2017 B · Q1. It mainly tests Linear equations, Rates (speed).

Kymbrea's comic book collection currently has 30 comic books in it, and she is adding to her collection at the rate of 2 comic books per month. LaShawn's collection currently has 10 comic books in it, and he is adding to his collection at the rate of 6 comic books per month. After how many months will LaShawn's collection have twice as many comic books as Kymbrea's?

Kymbrea 的漫画书收藏目前有 30 本漫画书，她每月以 2 本漫画书的速率增加收藏。LaShawn 的收藏目前有 10 本漫画书，他每月以 6 本漫画书的速率增加收藏。几个月后 LaShawn 的收藏将有 Kymbrea 收藏的两倍那么多？

(A) 1 1

(B) 4 4

(D) 20 20

(E) 25 25

Answer

Correct choice: (E)

正确答案：（E）

Solution

After $m$ months, Kymbrea’s collection will have $30 + 2m$ comic books and LaShawn’s collection will have $10 + 6m$ comic books. Solving $10 + 6m = 2(30 + 2m)$ yields $m = 25$, so LaShawn’s collection will have twice as many comic books as Kymbrea’s after 25 months.

经过 $m$ 个月后，Kymbrea 的收藏将有 $30 + 2m$ 本漫画书，LaShawn 的收藏将有 $10 + 6m$ 本漫画书。解方程 $10 + 6m = 2(30 + 2m)$ 得到 $m = 25$，因此 25 个月后 LaShawn 的收藏将是 Kymbrea 的两倍。

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