Question

The denominator of a fraction is five more than twice the numerator. If both the numerator and denominator are decreased by seven, the simplified result is 1/3. Find the original fraction.

Answer 1

THe fraction is:

 

 X

----------

2X + 5

 

 

Decreases the numerator and denominator by 1, the fraction becomes 3/8.

So now the fraction looks like this:

 

X-1                   3

--------- =  -----------

2x +5-1            8

 

Cross multiplies:

 

8(x-1) = 3 ( 2x +5 -1)

 

8x - 8 = 3( 2x + 4)

 

8x - 8 = 6x + 12  <--- distributive right side

 

8x - 8 - 6x - 12 = 0 <--- everybody moves left,changing signs, to keep leading coefficient of x term positive

 

2x - 20 = 0 <-- combines like terms

 

2x = 20 <--- solves for x

 

x=10

 

So the fraction 10/25.

 

(10-1)/(25-1) = 9/24 = 3/8