Find the original number

Question

The denominator of a fraction is 5 more than twice the numerator. If both numerator and denominator are decreased by 2, the simplified result is 1/3. Find the original fraction. (DO not simplify)

Answer 1

The first sentence can be represented by x/(5 + 2x).

 

Then we subtract 2 from the top and bottom and set that equal to 1/3

 

(x - 2)/(3 + 2x) = 1/3

 

Now solve for x by cross multiplying.

 

3(x - 2) = 3 + 2x

 

3x - 6 = 3 + 2x

 

x = 9

 

Plug this in to the first equation to get the original fraction.