Question

The numerator of a fraction is 3 less than its denominator. If the numerator is triplied and . the denominator is increased by 2, the value of the fraction obtained is 2:1. What was the original fraction?​

Answer 1

Let’s make notation n is numerator and d is denominator;

Are given initial fraction n/d; d=n+3, then the fraction may be rewritten as n/(n+3);

Next, (n+6)/(d+5)=(n+6)/(n+3+5)= (n+6)/(n+8), and this fraction equal doubled initial one, that is,

(n+6)/(n+8)= 2n/(n+3). After that we have one unknown and one equation, hence it can be solved.

Using cross sectional multiplication gives: n^2 +3n+6n+18=2n^2 +16n, and after simplification it gives quadratic equation.

n^2 + 7n-18=0 after factoring (n+9)(n-2)=0. Thus, n=-9 and n=+2.

Now, we can calculate d=n+3 that gives d=-6 and d=5.

Finally, the initial fraction -9/-6=9/6 and 2/5