SOLUTION: The denominator of a fraction is 9 more than its numerator. If the numerator and the denominator both are increased by 7, the new fraction becomes 10 7 . Find the original

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Question 1182962: The denominator of a fraction is 9 more than its numerator. If the numerator and the
denominator both are increased by 7, the new fraction becomes
10
7
. Find the original
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let numerator be x
if the denominator is 9 more than numerator, the denominator is x%2B9
fraction is:
x%2F%28x%2B9%29
if the numerator and the denominator both are increased by 7, the new fraction becomes 10%2F7
%28x%2B7%29%2F%28x%2B9%2B7%29=10%2F7............solve for x
%28x%2B7%29%2F%28x%2B16%29=10%2F7...., cross multiply
7%28x%2B7%29=10%28x%2B16%29
7x%2B49=10x%2B160
49-160=10x-7x
-111=3x
x=-111%2F3
x=-37-> numerator
the denominator is x%2B9=-37%2B9=-28
the original fraction is highlight%28-37%2F-28%29

check: the numerator and the denominator both are increased by 7
highlight%28%28-37%2B7%29%2F%28-28%2B7%29%29=10%2F7
highlight%28%28-30%29%2F%28-21%29%29=10%2F7
highlight%2830%2F21%29=10%2F7
highlight%2810%2F7%29=10%2F7