1959 AMC 12 Problem 24

Attempt Problem 24 of the 1959 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1959 AMC 12 solutions, or check the answer key.

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24.

A chemist has

m

ounces of salt water that is

m\%

salt. How many ounces of salt must he add to make a solution that is

2m\%

salt?

\dfrac{m}{100+m}

\dfrac{2m}{100-2m}

\dfrac{m^2}{100-2m}

\dfrac{m^2}{100+2m}

\dfrac{2m}{100+m}

The original amount of salt is

\frac{m^2}{100}

ounces

x

ounces of pure salt are added, equate

\frac{\frac{m^2}{100}+x}{m+x}

\frac{2m}{100}

Let

x

ounces of salt be added. The concentration equation is

\frac{\frac{m^2}{100}+x}{m+x}=\frac{2m}{100}.

Multiplying through and collecting the

x

-terms gives

x(100-2m)=m^2,

x=\frac{m^2}{100-2m}.

Therefore, the correct answer is C.

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