SOLUTION: The numerator equals the sum of the two digits in the denominator. The value of the fraction is 1/4. When both the numerator and denominator are increased by 3, the resulting fract

Algebra ->  Finance -> SOLUTION: The numerator equals the sum of the two digits in the denominator. The value of the fraction is 1/4. When both the numerator and denominator are increased by 3, the resulting fract      Log On


   

Question 886068: The numerator equals the sum of the two digits in the denominator. The value of the fraction is 1/4. When both the numerator and denominator are increased by 3, the resulting fraction has the value 1/3. Find the original fraction.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let n = the numerator.
let d = the denominator.
the value of the fraction is equal to 1/4 which means that n/d = 1/4
when both the numerator and denominator are increased by 3, the resulting fraction has the value of 1/3.
you get (n+3) / (d + 3) = 1/3
you have:
n/d = 1/4
(n+3)/(d+3) = 1/3
solve for n in both equations to get:
n = d/4
n = (d/3) - 2
set these 2 equations equal to each other to get:
d/4 = (d/3) - 2
subtract d/3 from both sides of the equation to get:
d/4 - d/3 = -2
multiply both sides of this equation by 12 to get:
3d - 4d = -24
simplify to get:
-d = -24
multiply both sides of this equation by -1 to get:
d = 24
since the numerator is equal to the sum of the 2 digits in the denominator, that means that n = 6.
your original fraction is equal to 6/24 which is equal to 1/4
add 3 to numerator and denominator and you get 9/27 which is equal to 1/3.
everything checks out.
your original fraction is equal to 6/24.

solving for n in (n+3) / (d+3) = 1/3 is done in the following manner.
start with:
(n+3) / (d+3) = 1/3
multiply both sides of this equation by (d+3) to get:
(n+3) = 1/3 * (d + 3)
simplify to get:
(n + 3) = (d/3) + 1
subtract 3 from both sides of this equation to get:
n = (d/3) + 1 - 3 which simplifies to:
n = (d/3) - 2