Question

一个罐子里有红色、绿色和蓝色弹珠。除了六个以外全是红弹珠，除了八个以外全是绿弹珠，除了四个以外全是蓝弹珠。罐子里有多少个弹珠？

In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?

$6$

$8$

$9$

$10$

$18$

答案：C

知识点：方程组

难度评级：1370

视频讲解：

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文字解答：

设红、绿、蓝弹珠数分别为 $r,g,b$ 。由题意可知把这些方程相加，得到 $3(r+g+b) -(r+g+b) = 18$ 。因此 $2(r+g+b) = 18$ ，所以 $r+g+b = 9$ 。也就是说，弹珠总数为 $9$ 。 $r+g+b -r=6,$ $r+g+b-g = 8,$ $r+g+b-b = 4$

所以正确答案是 C。

Let $r,g,b$ be the number of red marbles, green marbles, and blue marbles respectively. We then know $r+g+b -r=6,$ $r+g+b-g = 8,$ $r+g+b-b = 4$ by the statements given. Adding these equations yields $3(r+g+b) -(r+g+b) = 18.$ This would mean $2(r+g+b) = 18,$ so $r+g+b = 9.$ Therefore, the sum of all of the marbles is $9.$

Thus, the answer is C .

2012 AMC 8 第 19 题

答案：C

难度评级：1370

视频讲解：

文字解答：

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