The product of the numerator and denominator of a certain fraction is 588. What is the fraction if it is equivalent to 3/4?

Question

I know that the answer is 21/28, I'm just having trouble explaining how I got the answer.

Answer 1

n represents the numerator

d represents the denominator

 

n : d :: 3 : 4          proportion

3d = 4n                 product means/extremes

3d/4 = n                divide both sides by 4

 

n · d = 588           given

3d/4 · d = 588      substitute

3d²/4 = 588         simplify

3d² = 2352          multiply both sides by 4

d² = 784             divide both sides by 3

d = 28

 

What is the numerator?