AMC12 2013 A

AMC12 2013 A · Q5

AMC12 2013 A · Q5. It mainly tests Averages (mean), Arithmetic misc.

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 $t-d$?

汤姆、多萝西和萨米一起去度假，并同意平均分摊费用。在旅途中，汤姆支付了 \$105，多萝西支付了 \$125，萨米支付了 \$175。为了使费用平均分摊，汤姆给了萨米 $t$ 美元，多萝西给了萨米 $d$ 美元。求 $t-d$。

(A) 15 15

(B) 20 20

(D) 30 30

(E) 35 35

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The total shared expenses were $105 + 125 + 175 = 405$ dollars, so each traveler's fair share was $\frac{1}{3}\cdot 405 = 135$ dollars. Therefore $t = 135 - 105 = 30$ and $d = 135 - 125 = 10$, so $t - d = 30 - 10 = 20$.

答案（B）：共同分摊的总费用为 $105 + 125 + 175 = 405$ 美元，因此每位旅行者应分摊的公平份额是 $\frac{1}{3}\cdot 405 = 135$ 美元。因此 $t = 135 - 105 = 30$，且 $d = 135 - 125 = 10$，所以 $t - d = 30 - 10 = 20$。

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