AMC10 2014 A

AMC10 2014 A · Q2

AMC10 2014 A · Q2. It mainly tests Fractions, Averages (mean).

Roy's cat eats $\frac{1}{3}$ of a can of cat food every morning and $\frac{1}{4}$ 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?

Roy 的猫每天早上吃一罐猫粮的 $\frac{1}{3}$，每天晚上吃一罐猫粮的 $\frac{1}{4}$。在周一早上喂猫之前，Roy 打开了一盒含有 6 罐猫粮的盒子。猫在周几吃完了盒子里的所有猫粮？

(A) Tuesday 星期二

(B) Wednesday 星期三

(D) Friday 星期五

(E) Saturday 星期六

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Because Roy's cat eats $\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$ of a can of cat food each day, the cat eats 7 cans of cat food in 12 days. Therefore the cat eats $7-\frac{7}{12}=6\frac{5}{12}$ cans in 11 days and $6\frac{5}{12}-\frac{7}{12}=5\frac{5}{6}$ cans in 10 days. The cat finishes the cat food in the box on the 11th day, which is Thursday.

答案（C）：因为罗伊的猫每天吃 $\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$ 罐猫粮，所以这只猫在 12 天内吃完 7 罐猫粮。因此，这只猫在 11 天内吃 $7-\frac{7}{12}=6\frac{5}{12}$ 罐，在 10 天内吃 $6\frac{5}{12}-\frac{7}{12}=5\frac{5}{6}$ 罐。猫在第 11 天吃完盒子里的猫粮，这一天是星期四。

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