SOLUTION: The denominator of a fraction is four less than twice the numerator if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. What is the or

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: The denominator of a fraction is four less than twice the numerator if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. What is the or      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1036683: The denominator of a fraction is four less than twice the numerator if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. What is the original fraction?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let n = the numerator of the original fraction
let d = the denominator
:
Write an equation for each statement
:
The denominator of a fraction is four less than twice the numerator
d = 2n - 4
:
if three is added to both the numerator and denominator, the new fraction is equal to two-thirds.
%28%28n%2B3%29%29%2F%28%28d%2B3%29%29 = 2%2F3
cross multiply
3(n+3) = 2(d+3)
3n + 9 = 2d + 6
3n = 2d + 6 - 9
3n = 2d - 3
replace d = (2n-4)
3n = 2(2n-4) - 3
3n = 4n - 8 - 3
3n - 4n = -11
-n = -11
n = 11
Find d using the 1st equation d = 2n - 4
d = 2(11) - 4
d = 18
:
What is the original fraction? 11%2F18
:
:
You can check this for yourself, in the statement
"if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. "