SOLUTION: In a fraction, the numerator is 3 less than the denominator. If 1 is added to both the numerator and denominator, the value of the resulting fraction is 5/6. Find the original frac

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a fraction, the numerator is 3 less than the denominator. If 1 is added to both the numerator and denominator, the value of the resulting fraction is 5/6. Find the original frac      Log On


   

Question 722212: In a fraction, the numerator is 3 less than the denominator. If 1 is added to both the numerator and denominator, the value of the resulting fraction is 5/6. Find the original fraction.
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = the original denominator of the fraction
Then following the steps in the problem we get
(1) (d-3)/d becomes
(2) [(d-3)+1]/(d+1) = 5/6 or
(3) (d-2)/(d+1) = 5/6, and by cross multiplying we get
(4) 6*(d-2) = 5*(d+1) or
(5) 6d - 12 = 5d + 5 or
(6) d = 17
Check d using (2)
Is ([17-3+1]/(17+1) = 5/6)?
Is (15/18 = 5/6)?
Is (5/6 = 5/6)? Yes
Therefore the original numerator is three less than d or 14.
Answer: The original fraction is 14/17