2017 AMC 12B 第 1 题

先试着解答 2017 AMC 12B 第 1 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2017 AMC 12B 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

1.

Kymbrea 的漫画书收藏目前有 3030 本漫画书,并且她每月增加 22 本。LaShawn 的收藏目前有 1010 本漫画书,并且他每月增加 66 本。多少个月后,LaShawn 收藏的漫画书数量会是 Kymbrea 的两倍?
Kymbrea’s comic book collection currently has 3030 comic books in it, and she is adding to her collection at the rate of 22 comic books per month. LaShawn’s collection currently has 1010 comic books in it, and he is adding to his collection at the rate of 66 comic books per month. After how many months will LaShawn’s collection have twice as many comic books as Kymbrea’s?
11
44
55
2020
2525
答案:E
知识点:一次方程
小提示:
mm 个月后,两人的收藏分别有 30+2m30 + 2m 本和 10+6m10 + 6m 本漫画书
After mm months the collections hold 30+2m30 + 2m and 10+6m10 + 6m comic books
大提示:
列方程 10+6m=2(30+2m)10 + 6m = 2(30 + 2m),并解出 mm。
Set 10+6m=2(30+2m)10 + 6m = 2(30 + 2m) and solve for mm
解答:
mm 个月后,Kymbrea 有 30+2m30 + 2m 本漫画书,LaShawn 有 10+6m10 + 6m 本。令 10+6m=2(30+2m)10 + 6m = 2(30 + 2m),得到 10+6m=60+4m10 + 6m = 60 + 4m,因此 2m=502m = 50,m=25m = 25。
所以正确答案是 E。
After mm months, Kymbrea has 30+2m30 + 2m comic books and LaShawn has 10+6m.10 + 6m. Setting 10+6m=2(30+2m)10 + 6m = 2(30 + 2m) gives 10+6m=60+4m,10 + 6m = 60 + 4m, so 2m=502m = 50 and m=25.m = 25.
Thus, the correct answer is E.
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