1973 AMC 12 第 33 题

Question

向酸与水的混合物中加入一盎司水后，新混合物中酸占

20\%

。再向新混合物中加入一盎司酸后，所得混合物中酸占

33\frac13\%

。原混合物中酸的百分比为

When one ounce of water is added to a mixture of acid and water, the new mixture is

20\%

acid. When one ounce of acid is added to the new mixture, the result is

33\frac13\%

acid. The percentage of acid in the original mixture is

22\%

24\%

25\%

30\%

33\frac13\%

设原混合物中的水与酸分别为

x

盎司与

y

盎司

Let

x

and

y

be the original ounces of water and acid

加水后写一个浓度方程，再为随后加酸后的情况写另一个浓度方程

Write one concentration equation after adding water and another after subsequently adding acid

设原混合物含

x

盎司水和

y

盎司酸。两次添加给出

\begin{aligned} \frac{y}{x+y+1}&=\frac15,\\ \frac{y+1}{x+y+2}&=\frac13 \end{aligned}\text{。}

化简得

x+1=4y, \qquad x=2y+1\text{。}

因此

y=1

，

x=3

。原混合物中酸的百分比为

100\cdot\frac{y}{x+y} =100\cdot\frac14=25\%\text{。}

所以正确答案是 C。

Let the original mixture contain

x

ounces of water and

y

ounces of acid. The two additions give

\begin{aligned} \frac{y}{x+y+1}&=\frac15,\\ \frac{y+1}{x+y+2}&=\frac13. \end{aligned}

These simplify to

x+1=4y, \qquad x=2y+1.

Hence

y=1

and

x=3.

The original acid percentage was

100\cdot\frac{y}{x+y} =100\cdot\frac14=25\%.

Therefore, the correct answer is C.

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