SOLUTION: if 2 is added to the numerator and 3 to the denominator of a fraction, its value will be 3/4. if 3 is subtracted from the numerator and 1 from the denominator, its value will be 1/

Algebra ->  Linear-equations -> SOLUTION: if 2 is added to the numerator and 3 to the denominator of a fraction, its value will be 3/4. if 3 is subtracted from the numerator and 1 from the denominator, its value will be 1/      Log On


   

Question 1103438: if 2 is added to the numerator and 3 to the denominator of a fraction, its value will be 3/4. if 3 is subtracted from the numerator and 1 from the denominator, its value will be 1/4. What is the fraction?
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%28%28n%2B2%29%2F%28d%2B3%29=3%2F4%2C%28n-3%29%2F%28d-1%29=1%2F4%29


USING ALGEBRA.
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4%28n%2B2%29=3%28d%2B3%29
4n%2B8=3d%2B9
4n-3d=1
-
4%28n-3%29=d-1
4n-12=d-1
4n-d=11
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system%284n-3d=1%2C4n-d=11%29
%284n-d%29-4n%2B3d=11-1
2d=10
highlight%28d=5%29

4n-15=1
4n=16
n=4
OR
4n-5=11
4n=11%2B5
4n=16
highlight%28n=4%29

The fraction n%2Fd=highlight%284%2F5%29.



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What happens if you take each of those in reverse?
n%2Fd=%283-2%29%2F%284-3%29=1%2F1=1
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n%2Fd=%281%2B3%29%2F%284%2B1%29=4%2F5
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NO GOOD!

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor has the correct answer n=4 d=5 but his method of checking the answer is invalid.
(n+2)/(d+3)=3/4
(n-3)/(d-1)=1/4
substitute 4 for n and 5 for d
(4+2)/(5+3)=3/4
6/8=3/4
reduce 6/8
3/4=3/4
ok
(4-3)/(5-1)=1/4
1/4=1/4
ok