SOLUTION: the denominator of a fraction is 5 more than the numerator. if 5 is added to the numerator and 2 is added to the denominator, the value of the fraction is 8/9. find the original fr

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Question 119285: the denominator of a fraction is 5 more than the numerator. if 5 is added to the numerator and 2 is added to the denominator, the value of the fraction is 8/9. find the original fraction.
Answer by ankor@dixie-net.com(12701) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = original numerator
:
Just write an expression for what it says:
:
"the denominator of a fraction is 5 more than the numerator."
x%2F%28%28x%2B5%29%29
:
"if 5 is added to the numerator and 2 is added to the denominator,:
%28%28x%2B5%29%29%2F%28%28x%2B5%2B2%29%29 = %28%28x%2B5%29%29%2F%28%28x%2B7%29%29
:
"the value of the fraction is 8/9."
%28%28x%2B5%29%29%2F%28%28x%2B7%29%29 = 8%2F9
:
" find the original fraction."
:
Cross multiply and solve for x:
9(x+5) = 8(x+7)
:
9x + 45 = 8x + 56
:
9x - 8x = 56 - 45
:
x = 11
:
Original fraction: 11%2F16
:
Check solution using the statement:
"if 5 is added to the numerator and 2 is added to the denominator the value of the fraction is 8/9."
16%2F18 = 8%2F9 confirms out solution
:
How about this? Could you follow this OK? Any questions?