PLEASE!!! PLEASE!!!

Question

The numerator of a fraction is 15 less than twice its denominator. If the numerator is increased by 5 and the denominator is increased by 7, the new fraction will be equal to 2/3. What is the original fraction?

Answer 1

So the original fraction is (2x - 15) / x, with x representing the denominator.

 

If the numerator increases by 5, it becomes (2x - 10). If the denominator increases by 7, it becomes (x + 7), meaning that 2 / 3 = (2x - 10) / (x + 7). 

 

Expanding that out,

6x - 30 = 2x + 14

4x = 44

x= 11

 

The original fraction would then become

[(2 * 11) - 15] / 11

= (22 - 15) / 11

= 7 / 11