SOLUTION: a fraction will become 3 when the numerator is increased by 17; and the fraction will become 2/3 when the denominator is decreased by 1. find the fraction. let the fraction be x/y

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: a fraction will become 3 when the numerator is increased by 17; and the fraction will become 2/3 when the denominator is decreased by 1. find the fraction. let the fraction be x/y      Log On


   

Question 789283: a fraction will become 3 when the numerator is increased by 17; and the fraction will become 2/3 when the denominator is decreased by 1. find the fraction.
let the fraction be x/y
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B17%29%2Fy=3; and x%2F%28y-1%29=2%2F3.

Just solve the two simultaneous equations.
x%2B17=3y and 2%28y-1%29=3x
x%2B17=3y and 2y-2=3x
highlight%28x=3y-17%29 and substitute into the second equation as been formed:
2y-2=3%283y-17%29
2y-2=9y-3%2A17
-7y-2=-3%2A17
7y%2B2=3%2A17
7y=3%2A17-2=21%2B30-2=49
highlight%28y=7%29

x=3%2Ay-17=21-17=highlight%284%29