SOLUTION: The denominator of a fraction exceeds the numerator by 7. If the numerator is increased by three and the denominator increased by 5, the resulting fraction is equal to 1/2. Find

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The denominator of a fraction exceeds the numerator by 7. If the numerator is increased by three and the denominator increased by 5, the resulting fraction is equal to 1/2. Find       Log On


   

Question 663080: The denominator of a fraction exceeds the numerator by 7. If the numerator is increased by three and the denominator increased by 5, the resulting fraction is equal to 1/2. Find the original fraction.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
x = numerator
y = denominator
x = y+7
(x+3)/(y+5) = 1/2
Substitute x into the second equation
((y+7)+3)/(y+5) = 1/2
(y + 10) / (y + 5) = 1/2
Multiply both sides by (y+5)
y+10 = (y+5)/2
Multiply both sides by 2
2(y+10) = y+5
Distribute the 2
2y + 20 = y + 5
Group like terms
2y - y = 5 - 20
Combine like terms
y = -15
x = y+7 = -15+7 = -8
The original fraction is -8/-15
Proof
-8+3 = -5 and -15 + 5 = -10
-5/-10 = 1/2
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