Question

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

$22\%$

$24\%$

$25\%$

$30\%$

$33\frac13\%$

Answer: C

Concepts:mixture percentage system of equations

Difficulty rating: 1830

Small Hint:

Let $x$ and $y$ be the original ounces of water and acid

Big Hint:

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

Solution:

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.

1973 AMC 12 Problem 33

Answer: C

Difficulty rating: 1830

Small Hint:

Big Hint:

Solution:

Problem 33 in Other Years