SOLUTION: If the numerator and denominator of a fraction are each increased by 1, the result is 3/5; but if the numerator and denominator are each decreased by 1, the result is 5/9. Let the

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: If the numerator and denominator of a fraction are each increased by 1, the result is 3/5; but if the numerator and denominator are each decreased by 1, the result is 5/9. Let the      Log On


   

Question 723073: If the numerator and denominator of a fraction are each increased by 1, the result is 3/5; but if the numerator and denominator are each decreased by 1, the result is 5/9.
Let the fraction be a/b. Write down two equations satisfied by a and b:
(i)
(ii)
Find the fraction. a/b
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The +1 equation gives %28a%2B1%29%2F%28b%2B1%29=3%2F5, simplifying to 5a-3b=-2.
The -1 equation gives %28a-1%29%2F%28b-1%29=5%2F9, simplifying to 9a-5b=4.

You could solve both of those for a, equate the expressions and solve for b. Then substitute for b in either of the initial equations and find a.

ANSWER FOUND: a=11 and b=19.