Difference between revisions of "1950 AHSME Problems/Problem 23"
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A man buys a house for $10,000 and rents it. He puts <math>12\frac{1}{2}\%</math> of each month's rent aside for repairs and upkeep; pays $325 a year taxes and realizes <math>5\frac{1}{2}\%</math> on his investment. The monthly rent (in dollars) is: | A man buys a house for $10,000 and rents it. He puts <math>12\frac{1}{2}\%</math> of each month's rent aside for repairs and upkeep; pays $325 a year taxes and realizes <math>5\frac{1}{2}\%</math> on his investment. The monthly rent (in dollars) is: | ||
− | <math> \textbf{(A)}\ \64.82\qquad\textbf{(B)}\ \83.33\qquad\textbf{(C)}\ \72.08\qquad\textbf{(D)}\ \45.83\qquad\textbf{(E)}\ \177.08 </math> | + | <math> \textbf{(A)} \ \ 64.82\qquad\textbf{(B)} \ \ 83.33\qquad\textbf{(C)} \ \ 72.08\qquad\textbf{(D)} \ \ 45.83\qquad\textbf{(E)} \ \ 177.08 </math> |
== Solution == | == Solution == | ||
− | <math>12\frac{1}{2}\%</math> is the same as <math>\frac{1}{8}</math>, so the man sets one eighth of each month's rent aside, so he only gains <math>\frac{7}{8}</math> of his rent. He also pays $325 each year, and he realizes <math>5.5\%</math>, or $550, on his investment. Therefore he must have collected a total of $325 +$550 = $875 in rent. This was for the whole year, so he collected <math>\frac{875}{12}</math> dollars each month as rent. This is only <math>\frac{7}{8}</math> of the monthly rent, so the monthly rent in dollars is <math>\frac{875}{12}\cdot \frac{8}{7}=\boxed{\textbf{(B)}\ \83.33}</math> | + | <math>12\frac{1}{2}\%</math> is the same as <math>\frac{1}{8}</math>, so the man sets one eighth of each month's rent aside, so he only gains <math>\frac{7}{8}</math> of his rent. He also pays $325 each year, and he realizes <math>5.5\%</math>, or $550, on his investment. Therefore he must have collected a total of $325 +$550 = $875 in rent. This was for the whole year, so he collected <math>\frac{875}{12}</math> dollars each month as rent. This is only <math>\frac{7}{8}</math> of the monthly rent, so the monthly rent in dollars is <math>\frac{875}{12}\cdot \frac{8}{7}=\boxed{\textbf{(B)}\ \ 83.33}</math> |
== See Also == | == See Also == |
Revision as of 20:33, 27 January 2015
Problem
A man buys a house for $10,000 and rents it. He puts of each month's rent aside for repairs and upkeep; pays $325 a year taxes and realizes on his investment. The monthly rent (in dollars) is:
Solution
is the same as , so the man sets one eighth of each month's rent aside, so he only gains of his rent. He also pays $325 each year, and he realizes , or $550, on his investment. Therefore he must have collected a total of $325 +$550 = $875 in rent. This was for the whole year, so he collected dollars each month as rent. This is only of the monthly rent, so the monthly rent in dollars is
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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