AMC10 2013 A

AMC10 2013 A · Q5

AMC10 2013 A · Q5. It mainly tests Fractions, Averages (mean).

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 $t - d$?

Tom、Dorothy和Sammy去度假，同意平分费用。在旅行中Tom付了105美元，Dorothy付了125美元，Sammy付了175美元。为了平等分担费用，Tom给了Sammy $t$美元，Dorothy给了Sammy $d$美元。$t - d$是多少？

(A) 15 15

(B) 20 20

(D) 30 30

(E) 35 35

Answer

Correct choice: (B)

正确答案：（B）

Solution

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 $t -d = 30 -10 = 20$.

总共享费用为$105+125+175 = 405$美元，所以每人公平分担$\frac{1}{3} \cdot 405 = 135$美元。因此$t = 135-105 = 30$，$d = 135 -125 = 10$，所以$t -d = 30 -10 = 20$。

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