2008 AMC 8 第 9 题

先试着解答 2008 AMC 8 第 9 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 2008 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。

9.

20052005 年,投资大亨塔米投入了 $100\$100,为期两年。第一年她的投资亏损 15%15\%,但第二年剩余投资增长了 20%20\%。这两年内塔米的投资变化是多少?
In 20052005 Tycoon Tammy invested $100\$100 for two years. During the first year her investment suffered a 15%15\% loss, but during the second year the remaining investment showed a 20%20\% gain. Over the two-year period, what was the change in Tammy’s investment?
亏损 5%5\%
5%5\% loss
亏损 2%2\%
2%2\% loss
增长 1%1\%
1%1\% gain
增长 2%2\%
2%2\% gain
增长 5%5\%
5%5\% gain
答案:D
知识点:百分数
小提示:
亏损 15%15\% 后,剩下原投资的 85%85\%
After a 15%15\% loss, 85%85\% of the original investment remains.
大提示:
把 20%20\% 的增长作用在减少后的金额上,而不是原金额上
Apply the 20%20\% gain to the reduced amount, not to the original amount.
解答:
15%15\% 的亏损使投资从 $100\$100 变为 0.85⋅$100=$850.85\cdot\$100=\$85。
20%20\% 的增长再使其变为 1.2⋅$85=$1021.2\cdot\$85=\$102。
投资从 $100\$100 变为 $102\$102,也就是增长 2%2\%。
所以正确答案是 D。
The 15%15\% loss changes the investment from $100\$100 to 0.85⋅$100=$850.85\cdot\$100=\$85.
The 20%20\% gain then changes it to 1.2⋅$85=$1021.2\cdot\$85=\$102.
The investment went from $100\$100 to $102\$102, which is a 2%2\% gain.
Thus, D is the correct answer.
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