1997 AMC 8 第 18 题

先试着解答 1997 AMC 8 第 18 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 1997 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。

18.

上周杂货店小盒面巾纸的价格是 44 盒 $5\$5。本周促销价是 55 盒 $4\$4。促销期间每盒价格下降的百分比最接近
At the grocery store last week, small boxes of facial tissue were priced at 44 boxes for $5.\$5. This week they are on sale at 55 boxes for $4.\$4. The percent decrease in the price per box during the sale was closest to
30%30\%
35%35\%
40%40\%
45%45\%
65%65\%
答案:B
知识点:百分数速率
小提示:
百分比下降等于价格变化除以原价
Percent decrease is change divided by original price
大提示:
分别计算原来和促销时每盒的价格
Compute the old and sale prices per box
解答:
原来每盒价格为 $5÷4=$1.25。 \$ 5 \div 4 = \$ 1.25\text{。}
现在每盒价格为 $4÷5=$0.8。 \$ 4 \div 5 = \$ 0.8\text{。}
下降百分比为 1.25−0.81.25⋅100%=45125⋅100%=925⋅100%=36%。 \begin{gathered} \dfrac{1.25 - 0.8}{1.25} \cdot 100 \% \\ = \dfrac{45}{125} \cdot 100 \% \\ = \dfrac{9}{25} \cdot 100 \% \\ = 36 \% \end{gathered}\text{。}
所以正确答案是 B。
Originally, each box is worth $5÷4=$1.25. \$ 5 \div 4 = \$ 1.25.
Now, each box is worth $4÷5=$0.8. \$ 4 \div 5 = \$ 0.8.
The percent decrease is then 1.25−0.81.25⋅100%=45125⋅100%=925⋅100%=36%. \begin{gathered} \dfrac{1.25 - 0.8}{1.25} \cdot 100 \% \\ = \dfrac{45}{125} \cdot 100 \% \\ = \dfrac{9}{25} \cdot 100 \% \\ = 36 \%. \end{gathered}
Thus, B is the correct answer.
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