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

Explanation	Calculations	Help
$We first name variables for each of their current salaries.$	$R = Ron’s current salary C = Cathy’s current salary$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "3/5 of Ron’s current salary" into a mathematical expression and similarly translate "3/5 of Cathy’s current salary" into one.$	$\frac{3}{5} R \frac{3}{5} C$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the sum of their reduced salaries" into an addition and translate "will be equal to Cathy’s current salary" into an equality.$	$\frac{3}{5} R + \frac{3}{5} C = C$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We solve the equation to express Ron's current salary as a fraction of Cathy's current salary.$	$\frac{3}{5} R + \frac{3}{5} C = C \frac{3}{5} R = C - \frac{3}{5} C \frac{3}{5} R = \frac{2}{5} C R = \frac{2}{5} C \times \frac{5}{3} R = \frac{2}{3} C \frac{R}{C} = \frac{2}{3}$	Theory & Tactics Method Card EQUA1-A Click to view full details

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\frac{2}{3}

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

Explanation	Calculations	Help
$We first name variables for each of their current salaries.$	$R = Ron’s current salary C = Cathy’s current salary$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "3/5 of Ron’s current salary" into a mathematical expression and similarly translate "3/5 of Cathy’s current salary" into one.$	$\frac{3}{5} R \frac{3}{5} C$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the sum of their reduced salaries" into an addition and translate "will be equal to Cathy’s current salary" into an equality.$	$\frac{3}{5} R + \frac{3}{5} C = C$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We solve the equation to express Ron's current salary as a fraction of Cathy's current salary.$	$\frac{3}{5} R + \frac{3}{5} C = C \frac{3}{5} R = C - \frac{3}{5} C \frac{3}{5} R = \frac{2}{5} C R = \frac{2}{5} C \times \frac{5}{3} R = \frac{2}{3} C \frac{R}{C} = \frac{2}{3}$	Theory & Tactics Method Card EQUA1-A Click to view full details

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\frac{2}{3}