Question

Rob spends $\frac{1}{2}$ of his monthly paycheck, after taxes, on rent. He spends $\frac{1}{3}$ on food and $\frac{1}{8}$ on entertainment. If he donates the entire remainder, $500, to charity, what is Rob's monthly income, after taxes?

• A. 12,000$
• B. 13,200$
• C. 14,000$
• D. 15,000$

Answer 1

Answer: (B)

13,200$

You cannot use smart numbers in this problem, because it asks you for an actual dollar amount, not a variable expression, fraction, or percent. A portion of the total is specified, so there can be only one correct amount for that total. Clearly, if you assign a number to represent the total, you will not be able to accurately find the total.

First, use addition to find the fraction of Rob's money that he spends on rent, food, and entertainment:

$\frac{1}{2}+\frac{1}{3}+\frac{1}{8}=\frac{12}{24}+\frac{8}{24}+\frac{3}{24}=\frac{23}{24}$. Therefore, the $500thathedonatestocharityrepresents$\cfrac{1}{24}$ofhistotalmonthlypaycheck.Wecansetupaproportion:$\cfrac{500}{x} = \cfrac{1}{24}$.Thus,Robsmonthlyincomeis$ $500\times 24$, or 12,000$.