1994 AMC 12 第 16 题

Question

一个袋子里有一些红色弹珠，其余都是蓝色弹珠。若取走一颗红色弹珠，剩余弹珠中红色弹珠占七分之一；若不取走红色弹珠而改为取走两颗蓝色弹珠，剩余弹珠中红色弹珠占五分之一。袋子里原来有多少颗弹珠？

Some marbles in a bag are red and the rest are blue. If one red marble is removed, then one-seventh of the remaining marbles are red. If two blue marbles are removed instead of one red, then one-fifth of the remaining marbles are red. How many marbles were in the bag originally?

8

22

36

57

71

答案：B

知识点：systems of equations proportions

难度评级：1510

小提示：

设红色弹珠数为

R

，弹珠总数为

T

Let

R

be the red count and

T

the total count

大提示：

把两种操作分别写成

\frac{R-1}{T-1}=\frac{1}{7}

和

\frac{R}{T-2}=\frac{1}{5}

Translate the two experiments into

\frac{R-1}{T-1}=\frac{1}{7}

and

\frac{R}{T-2}=\frac{1}{5}

解答：

两个条件给出

\frac{R-1}{T-1}=\frac17

和

\frac{R}{T-2}=\frac15

。因此

T=7R-6

且

T=5R+2

。于是

R=4

，

T=22

。所以正确答案是 B。

The two conditions give

\frac{R-1}{T-1}=\frac17

and

\frac{R}{T-2}=\frac15.

Thus

T=7R-6

and

T=5R+2.

Hence

R=4

and

T=22.

Thus the correct answer is B.

1994 AMC 12 第 16 题

答案：B

难度评级：1510

小提示：

大提示：

解答：

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