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The value of the numerator of a particular fraction is one-half the value of its denominator. If the numerator is increased by 2 and the denominator is decreased by 2, the value of the resulting fraction is 3/4. What is the denominator of the original fraction?

 May 1, 2020
 #1
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Let the numberator  =  x

Then the denominator  = 2x

 

So...we have this

 

 x + 2                3

_______  =     ____           cross-multiply  

2x  - 2               4

 

 

 

4 ( x + 2)  = 3 (2x - 2)     simplify

 

4x + 8  =  6x  - 6         add 6 to both sides, subtract 4x from both sides

 

2x  = 14        divide both sides by 2

 

x  = 7

 

The denominator of the original fraction = 2x  = 2(7)   =  14

 

cool cool cool

 May 1, 2020

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