2012 AMC 12A 第 5 题

先试着解答 2012 AMC 12A 第 5 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 2012 AMC 12A 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。

5.

一份水果沙拉由蓝莓、覆盆子、葡萄和樱桃组成。水果沙拉中共有 280280 块水果。覆盆子的数量是蓝莓的两倍,葡萄的数量是樱桃的三倍,樱桃的数量是覆盆子的四倍。水果沙拉中有多少颗樱桃?
A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?
88
1616
2525
6464
9696
答案:D
知识点:比与比例方程组
小提示:
用蓝莓的数量表示每一种水果的数量
Express every count in terms of the number of blueberries
大提示:
若有 bb 颗蓝莓,则有 2b2b 颗覆盆子,8b8b 颗樱桃,24b24b 颗葡萄
With bb blueberries there are 2b2b raspberries, 8b8b cherries, and 24b24b grapes
解答:
设蓝莓有 bb 颗。则覆盆子有 2b2b 颗,樱桃有 4⋅2b=8b4 \cdot 2b = 8b 颗,葡萄有 3⋅8b=24b3 \cdot 8b = 24b 颗。
总数为 b+2b+8b+24b=35b=280b + 2b + 8b + 24b = 35b = 280,所以 b=8b = 8,樱桃有 8b=648b = 64 颗。
因此,正确答案是 D。
Let bb be the number of blueberries. Then there are 2b2b raspberries, 4⋅2b=8b4 \cdot 2b = 8b cherries, and 3⋅8b=24b3 \cdot 8b = 24b grapes.
The total is b+2b+8b+24b=35b=280,b + 2b + 8b + 24b = 35b = 280, so b=8b = 8 and there are 8b=648b = 64 cherries.
Thus, the correct answer is D.
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