Question

Tom、Dorothy 和 Sammy 去度假，并约定平均分摊费用。旅途中 Tom 支付了 $\$105$ ，Dorothy 支付了 $\$125$ ，Sammy 支付了 $\$175$ 。为了平摊费用，Tom 给 Sammy $t$ 美元，Dorothy 给 Sammy $d$ 美元。 $t - d$ 是多少？

Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $\$105,$ Dorothy paid $\$125,$ and Sammy paid $\$175.$ In order to share the costs equally, Tom gave Sammy $t$ dollars, and Dorothy gave Sammy $d$ dollars. What is $t - d?$

$15$

$20$

$25$

$30$

$35$

答案：B

知识点：平均数代数变形

难度评级：1130

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：

$t$ 和 $d$ 分别表示 Tom 和 Dorothy 比公平份额少付的金额

$t$ and $d$ measure how much Tom and Dorothy each fall short of their fair share

解答：

总花费为 $105 + 125 + 175 = 405$ ，所以每人的公平份额为 $\tfrac13\cdot 405 = 135$ 美元。

于是 $t = 135 - 105 = 30$ ， $d = 135 - 125 = 10$ ，所以 $t - d = 30 - 10 = 20$ 。

因此，正确答案是 B。

The total spent was $105 + 125 + 175 = 405,$ so each fair share is $\tfrac13\cdot 405 = 135$ dollars.

Then $t = 135 - 105 = 30$ and $d = 135 - 125 = 10,$ so $t - d = 30 - 10 = 20.$

Thus, the correct answer is B.

2013 AMC 12A 第 5 题

答案：B

难度评级：1130

小提示：

大提示：

解答：

其他年份的第 5 题