the orginal fraction

Question

The numerator of a certain fraction is five times the denominator. If 6 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. What was the original fraction ( not written in lowest terms)?

Answer 1

Let the original numerator = 5x

Let the original denominator = x

 

 

Set the equation using the variables and problem description.

 

(5x + 6) / (x + 6) = 2

 

 

Multiply both sides of the equation by (x + 6).

 

5x + 6 = 2(x + 6)

 

5x + 6 = 2x + 12

 

 

Subtract 2x on both sides of equation.

 

3x + 6 = 12

 

 

Subtract 6 on both sides of equation.

 

3x = 6

 

 

Divide both sides of the equation by 3.

 

x = 2

 

 

The denominator is 2.  The numerator is 10.

 

The original fraction is 10/2.