2013 AMC 10A 第 5 题

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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 一起度假,并同意平均分摊费用。旅途中 Tom 支付了 $105\$105,Dorothy 支付了 $125\$125,Sammy 支付了 $175\$175。为了平均分摊,Tom 给 Sammy tt 美元,Dorothy 给 Sammy dd 美元。tdt-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 costs equally, Tom gave Sammy tt dollars, and Dorothy gave Sammy dd dollars. What is td?t-d?

1515

2020

2525

3030

3535

答案:B
知识点:平均数钱币
难度评级:900
解答:

总费用为 $105+$125+$175=$405\$105+\$125+\$175=\$405,所以每人应承担 $405÷3=$135\$405\div3=\$135

Tom 少付 $30\$30,Dorothy 少付 $10\$10,因此 t=30t=30d=10d=10

所以 td=3010=20t-d=30-10=20

所以正确答案是 B

The total cost was $105+$125+$175=$405\$105+\$125+\$175=\$405, so each person's share was $405÷3=$135\$405\div3=\$135.

Tom paid $30\$30 less than his share, and Dorothy paid $10\$10 less than her share, so t=30t=30 and d=10d=10.

Therefore td=3010=20t-d=30-10=20.

Thus, B is the correct answer.

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