Difference between revisions of "1959 AHSME Problems/Problem 24"
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== Problem 24 == | == Problem 24 == | ||
| − | A chemist has m ounces of salt that is <math>m</math>% salt. How many ounces of salt must he add to make a solution that is <math>2m</math>% salt? | + | A chemist has m ounces of salt water that is <math>m</math>% salt. How many ounces of salt must he add to make a solution that is <math>2m</math>% salt? |
<math>\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}</math> | <math>\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}</math> | ||
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== Solution == | == Solution == | ||
There are <math>m</math> oz of salt, and there is <math>m\times\frac{m}{100}=\frac{m^2}{100}</math> oz of pure salt. We wish to add <math>k</math> oz of pure salt so that <math>\frac{m^2/100+k}{m+k}=\frac{2m}{100}</math>. Solving this results in <math>k=\frac{m^2}{100-2m}\rightarrow\boxed{\textbf{C}}</math> | There are <math>m</math> oz of salt, and there is <math>m\times\frac{m}{100}=\frac{m^2}{100}</math> oz of pure salt. We wish to add <math>k</math> oz of pure salt so that <math>\frac{m^2/100+k}{m+k}=\frac{2m}{100}</math>. Solving this results in <math>k=\frac{m^2}{100-2m}\rightarrow\boxed{\textbf{C}}</math> | ||
Latest revision as of 23:47, 30 December 2024
Problem 24
A chemist has m ounces of salt water that is 
% salt. How many ounces of salt must he add to make a solution that is 
% salt?
Solution
There are oz of salt, and there is 
oz of pure salt. We wish to add 
oz of pure salt so that 
. Solving this results in 
See also
| 1959 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
