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.

Algebra ->  Finance -> 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.      Log On


   

Question 1159720: 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.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The fraction n%2Fd

system%28%28n%2B3%29%2Fd=3%2F4%2Cn%2F%28d-7%29=1%29
All needed is solve this system for n and d.

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%28%28d-7%29%2B3%29%2Fd=3%2F4
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%28d-4%29%2Fd=3%2F4
4%28d-4%29=3d
4d-16=3d
d=16
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n=16-7
n=9


highlight%28n%2Fd=9%2F16%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A solution using logical reasoning and a bit of trial and error with simple arithmetic....

When the denominator is decreased by 7, the fraction becomes 1. That means the denominator is 7 more than the numerator. So the fraction is of the form n%2F%28n%2B7%29.

When the numerator is increased by 3, the fraction becomes (equivalent to) 3/4. So the fraction %28n%2B3%29%2F%28n%2B7%29 is equivalent to 3/4.

From there you can solve the problem algebraically:

%28n%2B3%29%2F%28n%2B7%29+=+3%2F4
3%28n%2B7%29+=+4%28n%2B3%29
3n%2B21+=+4n%2B12
n+=+9

The original fraction is n%2F%28n%2B7%29+=+9%2F16

If you have excellent number sense, you can also work the last part of the problem informally. You know the fraction %28n%2B3%29%2F%28n%2B7%29 is equivalent to 3/4. In the fraction 3/4, the difference between numerator and denominator is 1; you want the difference to be 4 (the difference between n+3 and n+7).

So the fraction after you increase the numerator by 3 is %283%2A4%29%2F%284%2A4%29+=+12%2F16; and that makes the original fraction 9/16.