SOLUTION: The denominator of a fraction is 8 more than the numerator. If both the numerator and denominator are decreased by 5, then the resulting fraction becomes 2/3. Find the original fra

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Question 1201447: The denominator of a fraction is 8 more than the numerator. If both the numerator and denominator are decreased by 5, then the resulting fraction becomes 2/3. Find the original fraction
Found 4 solutions by mananth, josgarithmetic, ikleyn, greenestamps:
Answer by mananth(16949) About Me  (Show Source):
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let x be the numerator
and y be the denominator
y= x+8
y-x =8 ................(1)
Both numerator and denominator decreased by 5
%28x-5%29%2F%28y-5%29+=2%2F3
3(x-5) = 2(y-5)
3x-15 = 2y-10

3x-2y=5................(2)
Multiply equation 1 by 2
we get
2y-2x=16 add this equation to 2
we get
2y-2x=16
3x-2y=5
x=21
y=x+8
y = 21+8=29
Fraction is 21/29



Answer by josgarithmetic(39749) About Me  (Show Source):
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Denominator, n+8
Numerator, n
Fraction: n%2F%28n%2B8%29

IF both decreased by,...
%28n-5%29%2F%28n%2B3%29=2%2F3

3%28n-5%29=2%28n%2B3%29
3n-15=2n%2B6
n=21

FRACTION IS 21%2F29 .

Answer by ikleyn(53646) About Me  (Show Source):
You can put this solution on YOUR website!
.
The denominator of a fraction is 8 more than the numerator. If both the numerator and denominator
are decreased by 5, then the resulting fraction becomes 2/3. Find the original fraction
~~~~~~~~~~~~~~~~~~~~~~~~~~


It can be easily solved using one unknown and one equation. 


Let x be the numerator of the fraction.

Then the denominator is (x+8).


Decreased values are (x-5) for the numerator and ((x+8)-5) = (x+3) for the denominator.


Write equation for modified fraction

    %28x-5%29%2F%28x%2B3%29 = 2%2F3.


Cross-multiply and find x

    3(x-5) = 2(x+3),

    3x - 15 = 2x + 6,

    3x - 2x = 6 + 15.

       x    =   21.


The original fraction is  21%2F%2821%2B8%29 = 21%2F29.    <<<---===  ANSWER

Solved.



Answer by greenestamps(13305) About Me  (Show Source):
You can put this solution on YOUR website!


A solution using logical reasoning instead of formal algebra....

When 5 is subtracted from both numerator and denominator of a fraction, the difference between the numerator and denominator remains unchanged.

In the fraction 2/3 that we want to end up with, the difference between the numerator and denominator is 1.

We need an equivalent fraction in which the numerator and denominator have a difference of 8. To find that fraction, simply multiply numerator and denominator of 2/3 by 8 to get the fraction 16/24.

That fraction 16/24 is the fraction we need to have after subtracting 5 from both numerator and denominator of the original fraction, so the original fraction is (16+5)/(24+5) = 21/29.

ANSWER: 21/29