+0  
 
0
427
1
avatar

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
 #1
avatar+87334 
+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

14 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.