SOLUTION: If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction.

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Question 196334: If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction.
Found 2 solutions by edjones, solver91311:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let n=numerator and d=denominator
a) (n+3)/d=3/4
b) n/(d+7)=1
b) n=d+7
a) (d+7+3)/d=3/4 substitute d+7 for n.
a) (d+10)/d=3/4
a) 4(d+10)=3d multiply each side by 4d
a) 4d+40=3d
d=-40
b) n=-40+7
n=-33
.
Ed

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let x represent the numerator of the original fraction. Let y represent the denominator of the original fraction. Then:



and



Cross-multiply both equations:



and



Solve the system. Substitution will work well here because you already have x defined in terms of y in the second equation.

John