How to solve GMAT Algebra Word Problems?

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?

1/3
2/5
1/2
3/5
2/3

1/3
2/5
1/2
3/5
2/3

Aarushi S · Accepted Answer

This one&rsquo;s just a linear equation disguised in word form. Let Ron&rsquo;s current salary be R and Cathy&rsquo;s be C. Their part-time salaries will be three-fifths of that, so Ron earns (3/5)R and Cathy earns (3/5)C.
The question says their reduced salaries add up to Cathy&rsquo;s full current salary, so:
(3/5)R + (3/5)C = C.
Factor out 3/5 on the left side:
(3/5)(R + C) = C.
Multiply both sides by 5 to eliminate the fraction:
3(R + C) = 5C &rarr; 3R + 3C = 5C &rarr; 3R = 2C.
Divide both sides by 3:
R = (2/3)C.
So Ron&rsquo;s salary is two-thirds of Cathy&rsquo;s. Correct answer is E.

kritika K · Answer

You can solve this with a quick equation and a bit of rearranging.

Let Ron&rsquo;s salary be R and Cathy&rsquo;s be C
Their reduced salaries are (3/5)R and (3/5)C, and the sum is equal to C
So: (3/5)R + (3/5)C = C &rarr; factor out 3/5: (3/5)(R + C) = C
Multiply both sides by 5: 3(R + C) = 5C &rarr; 3R + 3C = 5C
Subtract 3C: 3R = 2C &rarr; divide by 3: R = (2/3)C

Ron&rsquo;s salary is two-thirds of Cathy&rsquo;s. Correct option is E.