Question

If the same number is added to the nunerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?

Answer 1

x = 3

Explanation:

If the same number is added to the numerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?

`(12+x)/(13-x) =(3)/(2)`

multiply both sides by 13-x:

`(13-x)(12+x)/(13-x) =(3)/(2)(13-x)\\\\12+x = (3(13-x))/(2) \\\\12+x = (39-3x)/(2) \\`

multiply both sides by 2:

`2(12+x) = ((39-3x)/(2))\\\\24+2x = 39-3x`

subtract 24 from both sides:

24 + 2x - 24 = 39 - 3x - 24

2x = 15 - 3x

add 3 x to both sides:

2x + 3x = 15 - 3x + 3x

5x = 15

divide both sides by 5:

5x/5 = 15/5

x = 3

check:

`(12+x)/(13-x) =(3)/(2)\\\\(12+3)/(13-3) =(3)/(2)\\\\(15)/(10) =(3)/(2)\\\\(3)/(2) =(3)/(2)`