1988 AMC 8 第 23 题

先试着解答 1988 AMC 8 第 23 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 1988 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。

23.

玛丽亚以每 44 张 $5\$5 的价格买入电脑磁盘,并以每 33 张 $5\$5 的价格卖出。她必须卖出多少张电脑磁盘,才能获利 $100\$100?
Maria buys computer disks at a price of 44 for $5\$5 and sells them at a price of 33 for $5.\$5. How many computer disks must she sell in order to make a profit of $100?\$100?
100100
120120
200200
240240
12001200
答案:D
知识点:比与比例
小提示:
用 1212 张作为方便的一组,因为 1212 同时是 44 和 33 的倍数
Work with a convenient batch of 1212 disks, since 1212 is a multiple of both 44 and 33
大提示:
一打磁盘进价 $15\$15,售价 $20\$20,每打利润 $5\$5
A dozen disks costs $15\$15 and sells for $20,\$20, a profit of $5\$5 per dozen
解答:
按打计算磁盘,因为 1212 同时是 44 和 33 的倍数。一打磁盘买入需 3×$5=$153 \times \$5 = \$15,卖出可得 4×$5=$204 \times \$5 = \$20,每打利润为 $5\$5。
要获利 $100\$100,她需要 1005=20\dfrac{100}{5} = 20 打,也就是 20×12=24020 \times 12 = 240 张磁盘。
所以正确答案是 D。
Consider disks in dozens, since 1212 is a multiple of both 44 and 3.3. A dozen disks costs 3×$5=$153 \times \$5 = \$15 to buy and sells for 4×$5=$20,4 \times \$5 = \$20, for a profit of $5\$5 per dozen.
To make $100\$100 profit she needs 1005=20\dfrac{100}{5} = 20 dozen, which is 20×12=24020 \times 12 = 240 disks.
Thus, the correct answer is D .
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