1956 AMC 12 第 2 题

先试着解答 1956 AMC 12 第 2 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 1956 AMC 12 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。

2.

琼斯先生以每根 $1.20\$1.20 的价格卖出两根烟斗。按成本计算,其中一根获利 20%20\%,另一根亏损 20%20\%。在这笔交易中,他:
Mr. Jones sold two pipes at $1.20\$1.20 each. Based on the cost his profit on one was 20%20\% and his loss on the other was 20%.20\%. On the sale of the pipes, he:
收支相抵
broke even
亏损 44¢
lost 44¢
获利 44¢
gained 44¢
亏损 1010¢
lost 1010¢
获利 1010¢
gained 1010¢
答案:D
知识点:profit and lossreverse percentagescost price
小提示:
将售价除以 1.21.2 或 0.80.8,求出各自的成本
Recover each cost by dividing the sale price by 1.21.2 or 0.80.8
大提示:
将总成本与总售价 $2.40\$2.40 比较
Compare the combined cost with the combined selling price of $2.40\$2.40
解答:
获利 20%20\% 的烟斗成本为 $1.201.20=$1.00, \frac{\$1.20}{1.20}=\$1.00\text{,}而亏损 20%20\% 的烟斗成本为 $1.200.80=$1.50。 \frac{\$1.20}{0.80}=\$1.50\text{。}两根烟斗的总成本为 $2.50\$2.50,但总售价为 $2.40\$2.40,所以琼斯先生亏损 1010 美分。
因此,正确答案是 D。
The pipe sold at a 20%20\% profit cost $1.201.20=$1.00, \frac{\$1.20}{1.20}=\$1.00, while the pipe sold at a 20%20\% loss cost $1.200.80=$1.50. \frac{\$1.20}{0.80}=\$1.50. Their combined cost was $2.50,\$2.50, but they sold for $2.40,\$2.40, so Mr. Jones lost 1010 cents.
Thus, the correct answer is D.
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