2009 AMC 8 第 1 题

先试着解答 2009 AMC 8 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 2009 AMC 8 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.

布里奇特在杂货店买了一袋苹果。她把一半苹果给了安。然后她给了凯茜 33 个苹果,自己留下 44 个苹果。布里奇特买了多少个苹果?
Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie 33 apples, keeping 44 apples for herself. How many apples did Bridget buy?
33
44
77
1111
1414
答案:E
知识点:逆推法
小提示:
从布里奇特自己留下和给凯茜的苹果数倒推
Work backward from the apples Bridget kept and gave to Cassie.
大提示:
这些苹果就是没有给安的那一半
Those apples were the half not given to Ann.
解答:
可以倒推,从布里奇特自己留下的 44 个苹果开始。加上她给凯茜的 33 个苹果,这一半共有 77 个苹果。
因为她把原来苹果的一半给了安,所以再乘以 22。7⋅2=147 \cdot 2 = 14,因此布里奇特一开始有 1414 个苹果。
所以正确答案是 E。
We can work backwards, starting with the 44 apples that Bridget kept for herself. Adding the 33 apples that she gave Cassie, she now has 77 apples.
Finally, we multiply this value by 22 since she gave half of her initial apples to Ann. 7⋅2=14,7 \cdot 2 = 14, so Bridget started off with 1414 apples.
Thus, E is the correct answer.
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