Next month, Ron and Cathy will each begin working part-time at 3/5...

Question

Next month, Ron and Cathy will each begin working part-time at 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?

GMAT Panda · Accepted Answer

2/3 We first name variables for each of their current salaries. R = Ron's current salary C = Cathy's current salary We translate "3/5 of Ron's current salary" into a mathematical expression and similarly translate "3/5 of Cathy's current salary" into one. 3/5R 3/5C We translate "the sum of their reduced salaries" into an addition and translate "will be equal to Cathy's current salary" into an equality. 3/5R + 3/5C = C We solve the equation to express Ron's current salary as a fraction of Cathy's current salary. 3/5R + 3/5C = C 3/5R = C - 3/5C 3/5R = 2/5C R = 2/5C 5/3 R = 2/3C R/C = 2/3

Explanation	Calculations	Help
$We first name variables for each of their current salaries.$	$R = Ron’s current salary C = Cathy’s current salary$
$We translate "3/5 of Ron’s current salary" into a mathematical expression and similarly translate "3/5 of Cathy’s current salary" into one.$	$\frac{3}{5} R \frac{3}{5} C$
$We translate "the sum of their reduced salaries" into an addition and translate "will be equal to Cathy’s current salary" into an equality.$	$\frac{3}{5} R + \frac{3}{5} C = C$
$We solve the equation to express Ron's current salary as a fraction of Cathy's current salary.$	$\frac{3}{5} R + \frac{3}{5} C = C \frac{3}{5} R = C - \frac{3}{5} C \frac{3}{5} R = \frac{2}{5} C R = \frac{2}{5} C \times \frac{5}{3} R = \frac{2}{3} C \frac{R}{C} = \frac{2}{3}$

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