Question

Roy 的猫每天早上吃 $\dfrac{1}{3}$ 罐猫粮，每天晚上吃 $\dfrac{1}{4}$ 罐猫粮。星期一早上喂猫之前，Roy 打开一个装有 $6$ 罐猫粮的盒子。这只猫在星期几吃完盒子里所有猫粮？

Roy’s cat eats $\dfrac{1}{3}$ of a can of cat food every morning and $\dfrac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing $6$ cans of cat food. On what day of the week did the cat finish eating all the cat food in the box?

星期二

Tuesday

星期三

Wednesday

星期四

Thursday

星期五

Friday

星期六

Saturday

答案：C

知识点：速率分数日期与时间

难度评级：1140

小提示：

这只猫每天共吃 $\frac7{12}$ 罐。

The cat eats $\frac7{12}$ can per full day

大提示：

找出累计吃掉 $6$ 罐时落在哪一天。

Check the integer day when the total first reaches $6$ cans

解答：

这只猫每个完整的一天共吃 $\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}$ 罐猫粮。经过 $10$ 个完整的一天，它吃了 $10\cdot\frac7{12}=\frac{35}{6}$ 罐，还剩 $\frac16$ 罐。

它会在下一次早晨喂食时吃完剩余部分。从星期一算作第一个早晨，第十一个早晨是星期四。

所以正确答案是 C。

The cat eats $\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}$ cans of food each full day. After $10$ full days, it has eaten $10\cdot\frac7{12}=\frac{35}{6}$ cans, leaving $\frac16$ of a can.

The cat finishes that remainder during its next morning feeding. The eleventh morning, counting Monday as the first, is Thursday.

Thus, C is the correct answer.

2014 AMC 10A 第 2 题

答案：C

难度评级：1140

小提示：

大提示：

解答：

其他年份的第 2 题