SOLUTION: the denominator of a fraction is 4 more than the numerator. If 3 is added to both the numerator and denominator, the new fraction is 2/3. What is the original fraction?

Question 1190756: the denominator of a fraction is 4 more than the numerator. If 3 is added to both the numerator and denominator, the new fraction is 2/3. What is the original fraction?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x be the numerator and y be the denominator.
the fraction is x/y.
you are given that the denominator is 4 more than the numerator.
xince y = x + 4, the fraction becomes:
x/(x+4)
you are given that when 3 is added to both the numerator and the denominator, the fraction is 2/3.
this gets you:
(x + 3) / (x + 4 + 3) = 2/3
simplify to get:
(x + 3) / (x + 7) = 2/3
cross multiply to get:
3 * (x + 3) = 2 * (x + 7)
simplify to get:
3x + 9 = 2x + 14
subtract 2x from both sides and subtract 9 from both sides to get:
x = 5
since y = 4 more than that, you get:
x = 5
y = 9
the original fraction is x/y = 5/9
add 3 to the numerator and he denominator to get 8/12 which is equal to 2/3.
this confirms the solution is correct.
the solution is that the original fraction is 5/9.

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