Question

Tony 每天工作 $2$ 小时，并且每满一岁，每小时工资为 $\$0.50$ 。在六个月期间，Tony 工作了 $50$ 天，赚了 $\$630$ 。这六个月结束时 Tony 几岁？

Tony works $2$ hours a day and is paid $\$0.50$ per hour for each full year of his age. During a six month period Tony worked $50$ days and earned $\$630.$ How old was Tony at the end of the six month period?

$9$

$11$

$12$

$13$

$14$

答案：D

知识点：年龄问题速率极限情形界定

难度评级：1370

解答：

Tony 共工作了 $2\cdot50=100$ 小时，所以平均时薪是 $\$630\div100=\$6.30.$ 因为他的时薪等于其整岁年龄乘以 $\$0.50$ ，所以工作日的平均年龄是 $6.30\div0.50=12.6$ 岁。在六个月内，他的年龄最多变化一岁，因此他必定有些工作日在 $12$ 岁，有些在 $13.$ 岁。所以这段时间结束时他是 $13$ 岁。

所以正确答案是 D。

Tony worked $2\cdot50=100$ hours, so his average hourly pay was $\$630\div100=\$6.30.$ Because his hourly pay is $\$0.50$ times his age in full years, his average age on the days he worked was $6.30\div0.50=12.6$ years. During a six-month period his age can change by at most one, so he must have worked some days at age $12$ and some at age $13.$ Thus he was $13$ at the end of the period.

Thus, D is the correct answer.

2010 AMC 10A 第 8 题

答案：D

难度评级：1370

解答：

其他年份的第 8 题