SOLUTION: The denominator of a fraction is 5 more than the numerator. If both the numerator and denominator are decreased by 2, the resulting fraction is equivalent to 7/12. Find the fractio

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: The denominator of a fraction is 5 more than the numerator. If both the numerator and denominator are decreased by 2, the resulting fraction is equivalent to 7/12. Find the fractio      Log On


   

Question 666968: The denominator of a fraction is 5 more than the numerator. If both the numerator and denominator are decreased by 2, the resulting fraction is equivalent to 7/12. Find the fraction.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Establish variables
x = numerator
y = denominator
...
Given
y = x+5
%28x-2%29%2F%28y-2%29+=+7%2F12
...
Substitute y into the second equation
%28x-2%29%2F%28%28x%2B5%29-2%29+=+7%2F12
...
Cross multiply
12(x-2) = 7((x+5)-2)
12x - 24 = 7x + 35 - 14
...
Combine like terms
12x - 7x = 35 - 14 + 24
5x = 45
x = 9
...
y = x+5 = 9+5 = 14
...
highlight_green%289%2F14%29
Which was the long way of seeing that
%287%2B2%29%2F%2812%2B2%29+=+9%2F14
.....................
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