1950 AMC 12 Problem 23

Attempt Problem 23 of the 1950 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 1950 AMC 12 solutions, or check the answer key.

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23.

A man buys a house for $\$10{,}000$ and rents it. He puts $12\dfrac12\%$ of each month’s rent aside for repairs and upkeep; pays $\$325$ a year taxes and realizes $5\dfrac12\%$ on his investment. The monthly rent is:

$\$64.82$

$\$83.33$

$\$72.08$

$\$45.83$

$\$177.08$

Answer: B

Concepts:money percentage linear equation

Difficulty rating: 1650

Small Hint:

Let $r$ be the monthly rent and express the annual rent as $12r$

Big Hint:

After upkeep and taxes, the annual return must be $5.5\%$ of $\$10,000$

Solution:

Let the monthly rent be $r$ dollars. The yearly rent is $12r,$ of which $1-0.125=\tfrac78$ remains after setting aside the upkeep money. The desired yearly return is $0.055(10,000)=550$ dollars, so $\frac78(12r)-325=550.$ Hence $10.5r=875,$ giving $r=83.\overline3,$ which is $\$83.33$ to the nearest cent.

Thus, the correct answer is B.

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Full Exam

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