AMC8 2012

AMC8 2012 · Q19

AMC8 2012 · Q19. It mainly tests Systems of equations, Logic puzzles.

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?

一个装有红、绿、蓝三色小圆珠的罐子，除了6颗是红的，其余都是红的；除了8颗是绿的，其余都是绿的；除了4颗是蓝的，其余都是蓝的。罐子里共有多少颗小圆珠？

(A) 6 6

(B) 8 8

(D) 10 10

(E) 18 18

Answer

Correct choice: (C)

正确答案：（C）

Solution

$6$ are blue and green - $b+g=6$ $8$ are red and blue - $r+b=8$ $4$ are red and green - $r+g=4$ We can do trial and error. Let's make blue $5$. That makes green $1$ and red $3$ because $6-5=1$ and $8-5=3$. To check this, let's plug $1$ and $3$ into $r+g=4$, which works. Now count the number of marbles - $5+3+1=9$. So the answer is $\boxed{\textbf{(C)}\ 9}.$

$6$ 颗是蓝和绿 - $b+g=6$ $8$ 颗是红和蓝 - $r+b=8$ $4$ 颗是红和绿 - $r+g=4$ 我们可以试值。设蓝为 $5$，则绿为 $1$，红为 $3$，因为 $6-5=1$，$8-5=3$。检查 $r+g=4$，$3+1=4$，成立。总颗数 $5+3+1=9$。因此答案是 $\boxed{\textbf{(C)}\ 9}$。

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