SOLUTION: The numerator of a fraction is 2 more than the denominator. If denominator is doubled at the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3. F

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The numerator of a fraction is 2 more than the denominator. If denominator is doubled at the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3. F      Log On


   

Question 599990: The numerator of a fraction is 2 more than the denominator. If denominator is doubled at the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3. Find the original fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The numerator of a fraction is 2 more than the denominator.
If denominator is doubled and the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3.
Find the original fraction.
:
Let x = the denominator
then
(x+2) = the numerator
:
%28%28x%2B2%29%29%2Fx = the original fraction
:
the equation for the statement:
"If denominator is doubled and the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3."
%28%28x%2B1%29%29%2F%282x%29 + %28%28x%2B2%29%29%2Fx = 7%2F3
Multiply by 6x
6x*%28%28x%2B1%29%29%2F%282x%29 + 6x*%28%28x%2B2%29%29%2Fx = 6x*7%2F3
cancel the denominators and you have
3(x+1) + 6(x+2) = 2x(7)
3x + 3 + 6x + 12 = 14x
9x + 15 = 14x
15 = 14x - 9x
15 = 5x
x = 15/5
x = 3
:
5%2F3 is the original fraction