Question

一个容量为 $16$ 夸脱的散热器中装满了水。取出四夸脱并补入纯防冻液；再从混合液中取出四夸脱并补入纯防冻液。如此再进行第三次和第四次。最终混合液中水所占的比例为：

A $16$ -quart radiator is filled with water. Four quarts are removed and replaced with pure antifreeze liquid. Then four quarts of the mixture are removed and replaced with pure antifreeze. This is done a third and a fourth time. The fractional part of the final mixture that is water is:

$\dfrac14$

$\dfrac{81}{256}$

$\dfrac{27}{64}$

$\dfrac{37}{64}$

$\dfrac{175}{256}$

答案：B

知识点：混合问题等比数列过程模拟

难度评级：1280

小提示：

每次取出混合液，都会带走当前剩余水的相同比例

Each removal takes away the same fraction of whatever water remains

大提示：

每次更换后，原有水量的 $\frac{3}{4}$ 留下

After one replacement, $\frac{3}{4}$ of the previous water remains

解答：

每次取出充分混合的散热器内容物的四分之一，因此留下当时水量的四分之三。四次更换后，水所占的比例为 $\left(\frac34\right)^4=\frac{81}{256}\text{。}$

所以正确答案为 B。

Each removal takes one-fourth of the well-mixed radiator contents, so it leaves three-fourths of the water then present. After four replacements, the water fraction is $\left(\frac34\right)^4=\frac{81}{256}.$

Therefore, the correct answer is B.

1958 AMC 12 第 28 题

答案：B

难度评级：1280

小提示：

大提示：

解答：

其他年份的第 28 题