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 $k=\frac{m^2}{100-2m}\rightarrow\boxed{\textbf{C}}$

See also

1959 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png