GMAT Practice Question: Next month, Ron and Cathy will each begin working part-time at \frac{3}{5}...
Question
Next month, Ron and Cathy will each begin working part-time at \frac{3}{5} of their respective current salaries. If the sum of their reduced salaries will be equal to Cathy's current salary, then Ron's current salary is what fraction of Cathy's current salary?
- \frac{1}{3}
- \frac{2}{5}
- \frac{1}{2}
- \frac{3}{5}
- \frac{2}{3}
Topics: word problems, fractions, linear equations, translations
Solution
Step 1
We first name variables for each of their current salaries.
R = \text{Ron's current salary} C = \text{Cathy's current salary}
Step 2
We translate \textbf{\text{"3/5 of Ron's current salary"}} into a mathematical expression and similarly translate \textbf{\text{"3/5 of Cathy's current salary"}} into one.
\frac{3}{5}R \frac{3}{5}C
Step 3
We translate \textbf{\text{"the sum of their reduced salaries"}} into an addition and translate \textbf{\text{"will be equal to Cathy's current salary"}} into an equality.
\frac{3}{5}R + \frac{3}{5}C = C
Step 4
We solve the equation to express Ron's current salary as a fraction of Cathy's current salary.
\frac{3}{5}R + \frac{3}{5}C = C \frac{3}{5}R = C - \frac{3}{5}C \frac{3}{5}R = \frac{2}{5}C R = \frac{2}{5}C \times \frac{5}{3} R = \frac{2}{3}C \frac{R}{C} = \frac{2}{3}
Answer
\frac{2}{3}
