2014 AMC 12A 第 2 题

先试着解答 2014 AMC 12A 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 2014 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。

2.

在剧院,儿童票半价。55 张成人票和 44 张儿童票共 $24.50\$24.50。88 张成人票和 66 张儿童票要花多少钱?
At the theater children get in for half price. The price for 55 adult tickets and 44 child tickets is $24.50.\$24.50. How much would 88 adult tickets and 66 child tickets cost?
$35\$35
$38.50\$38.50
$40\$40
$42\$42
$42.50\$42.50
答案:B
知识点:比与比例
小提示:
儿童票是成人票的一半,所以把所有票都换算成成人票。
A child ticket costs half an adult ticket, so measure everything in adult tickets
大提示:
5+12⋅4=75+\tfrac12\cdot4=7 张成人票花 $24.50\$24.50;再求 8+12⋅6=118+\tfrac12\cdot6=11 张成人票的费用。
5+12⋅4=75+\tfrac12\cdot4=7 adult tickets cost $24.50\$24.50; find the cost of 8+12⋅6=118+\tfrac12\cdot6=11 adult tickets
解答:
儿童票半价,所以 55 张成人票和 44 张儿童票相当于 5+12⋅4=75+\tfrac12\cdot4=7 张成人票,因此一张成人票价格为 24.507=$3.50\dfrac{24.50}{7}=\$3.50。
第二次购买相当于 8+12⋅6=118+\tfrac12\cdot6=11 张成人票,费用为 11⋅3.50=$38.5011\cdot 3.50=\$38.50。
所以正确答案是 B。
Since a child ticket is half an adult ticket, 55 adult and 44 child tickets equal 5+12⋅4=75+\tfrac12\cdot4=7 adult tickets, so one adult ticket costs 24.507=$3.50.\dfrac{24.50}{7}=\$3.50.
The second purchase equals 8+12⋅6=118+\tfrac12\cdot6=11 adult tickets, costing 11⋅3.50=$38.50.11\cdot 3.50=\$38.50.
Thus, the correct answer is B.
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