SOLUTION: If the numerator and denominator of a certain fraction are increased by 1, the value of the fraction is 1/2. if the numerator of the original fraction is left unchanged and the den

Algebra ->  Equations -> SOLUTION: If the numerator and denominator of a certain fraction are increased by 1, the value of the fraction is 1/2. if the numerator of the original fraction is left unchanged and the den      Log On


   

Question 698704: If the numerator and denominator of a certain fraction are increased by 1, the value of the fraction is 1/2. if the numerator of the original fraction is left unchanged and the denominator is increased by 3, the value of the fraction is 1/4. Find the original fraction.

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Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
let numerator be x and denominator be y, then our fraction is x/y. Now we follow the problem and create equauations
%28x%2B1%29%2F%28y%2B1%29=1%2F2
x%2F%28y%2B3%29=1%2F4
we multiply each equation across and get
2(x+1)=y+1
4x=y+3
********simplify first equaiton
2x+2=y+1
4x=y+3
********subtract 2 from each side on the first equation
2x=y-1
4x=y+3
********multiply first equation by -2
-4x=-2y+2
4x=y+3
**********add the two equations
0=-y+5 add y to each side
y=5
now we plug that into any of the equations since they are all true and solve for x, i'll use the 4x=y+3 equation
4x=5+3
4x=8 divide each side by 4
x=2
so we said original fraction was x/y so 2/5