1959 AHSME Problems/Problem 24

Problem 24

A chemist has m ounces of salt that is $m$ % salt. How many ounces of salt must he add to make a solution that is $2m$ % salt?

$\textbf{(A)}\ \frac{m}{100+m} \qquad\textbf{(B)}\ \frac{2m}{100-2m}\qquad\textbf{(C)}\ \frac{m^2}{100-2m}\qquad\textbf{(D)}\ \frac{m^2}{100+2m}\qquad\textbf{(E)}\ \frac{2m}{100+2m}$

Solution

There are $m$ oz of salt, and there is $m\times\frac{m}{100}=\frac{m^2}{100}$ oz of pure salt. We wish to add $k$ oz of pure salt so that $\frac{m^2/100+k}{m+k}=\frac{2m}{100}$ . Solving this results in $k=\frac{m^2}{100-2m}\rightarrow\boxed{\textbf{C}}$

1959 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
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1959 AHSME Problems/Problem 24

Problem 24

Solution

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