2013 AMC 12A 第 5 题

先试着解答 2013 AMC 12A 第 5 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 2013 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。

5.

Tom、Dorothy 和 Sammy 去度假,并约定平均分摊费用。旅途中 Tom 支付了 $105\$105,Dorothy 支付了 $125\$125,Sammy 支付了 $175\$175。为了平摊费用,Tom 给 Sammy tt 美元,Dorothy 给 Sammy dd 美元。t−dt - d 是多少?
Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105,\$105, Dorothy paid $125,\$125, and Sammy paid $175.\$175. In order to share the costs equally, Tom gave Sammy tt dollars, and Dorothy gave Sammy dd dollars. What is t−d?t - d?
1515
2020
2525
3030
3535
答案:B
知识点:平均数代数变形
小提示:
每个人公平应付的金额是总花费的三分之一
Each person’s fair share is one third of the total spent
大提示:
tt 和 dd 分别表示 Tom 和 Dorothy 比公平份额少付的金额
tt and dd measure how much Tom and Dorothy each fall short of their fair share
解答:
总花费为 105+125+175=405105 + 125 + 175 = 405,所以每人的公平份额为 13⋅405=135\tfrac13\cdot 405 = 135 美元。
于是 t=135−105=30t = 135 - 105 = 30,d=135−125=10d = 135 - 125 = 10,所以 t−d=30−10=20t - d = 30 - 10 = 20。
因此,正确答案是 B。
The total spent was 105+125+175=405,105 + 125 + 175 = 405, so each fair share is 13⋅405=135\tfrac13\cdot 405 = 135 dollars.
Then t=135−105=30t = 135 - 105 = 30 and d=135−125=10,d = 135 - 125 = 10, so t−d=30−10=20.t - d = 30 - 10 = 20.
Thus, the correct answer is B.
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