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The denominator of a fraction in simplest form is greater than the numerator by 3. If 7 is added to the numerator, and 5 added to the denominator, then the fraction itself is increased by

1/2

. Find the original fraction.

Guest Mar 10, 2017
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 #1
avatar+79881 
+5

Let the original fraction = n / [n + 3]

 

And we have that

 

[n + 7] / [n + 8]  =  n / [n + 3]  + 1/2

 

[ n + 7] / [n + 8]  =  [ 2n + n + 3] / [ 2(n + 3) ]   cross-multiply

 

[2(n +3)] [ n + 7]= [2n + n + 3] [ n + 8]

 

[2(n +3)] [ n + 7]= [3n + 3] [ n + 8]

 

2 [ n + 3] [ n + 7 ] = 3 [n + 1] [ n + 8 ]

 

2 [ n ^2 + 10n + 21] = 3 [ n^2 + 9n + 8]

 

2n^2 + 20n + 42  =  3n^2 + 27n + 24    

 

n ^2 + 7n - 18  = 0       factor

 

(n + 9) ( n - 2)   = 0      and n  = -9 or n = 2

 

So....one possibility...when n = 2

 

9 / 10  = 2/5 + 1/2

 

9/10  = 9/10

 

Or  when  n = -9

 

-2/-1  = -9/-6 + 1/2

 

2  =  3/2 + 1/2

 

2 = 2

 

So....the original fractions were   2/5   or 3/2

 

 

cool cool cool

CPhill  Mar 10, 2017

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