Question

Lisa spends $\frac{8}{3}$ of her monthly paycheck on rent and $\frac{5}{12}$ on food. Her roommate, Carrie,who earns twice as much as Lisa, spends $\frac{1}{4}$ of her monthly paycheck on rent and $\frac{1}{2}$ on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate?

• A. $\frac{3}{8}$
• B. $\frac{17}{72}$
• C. $\frac{17}{48}$
• D. $\frac{13}{72}$

Answer 1

Answer: (B)

$\frac{17}{72}$

Use smart numbers to solve this problem. Since the denominators in the problem are 8, 12, 4, and 2, assign Lisa a monthly paycheck of $24.Assignherroommate,whoearnstwiceasmuch,amonthlypaycheckof$48. The two women's monthly expenses break down as follows:

Rent Food Left over

Lisa $\frac{3}{8}$ of 24 = 9 $\frac{5}{12}$ of 24 = 10 $24-(9+10)=5$

Carrie $\frac{1}{4}$ of 48 = 12 $\frac{1}{2}$ of 48 = 24 $48-(12+24)=12$

The women will donate a total of $17outoftheircombinedmonthlyincomeof$72.

So, they will donate $\frac{17}{72}$ portion to the charity.