Difference between revisions of "1950 AHSME Problems/Problem 23"
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| − | ==Problem== | + | == Problem == |
| − | A man buys a house for | + | 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 | + | <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 == | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:55, 11 October 2020
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 | |
| 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. 
