# What are the numerator and denominator of a fraction if them ratio is 3/4 ?If subtracting 8 from numerator and adding 8 to denominator the ratio is 1/6.

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We are given given that the ratio of the numerator and the denominator is 3/4

Let the numerator be N and the denominator be D

N/ D = 3/4

=> N = (3/4)*D

(N - 8)/ ( D + 8) = 1/6

=> 6N - 48 = D + 8

=> 6*(3D / 4) = D + 56

=> 9D/2 = D + 56

=> 9D / 2 - 2D / 2 = 56

=> 7D / 2 = 56

=> D = 56*2 / 7

=> D = 16

N = (3/4)*D = (3/4)*16 = 12

**The numerator is 12 and the denominator is 16.**

The numbers are x and y.

We'll write the first fraction x/y = 3/4.

x = 3y/4

We'll write mathematically the second condition from enunciation:

(x-8)/(y+8) = 1/6

y + 8 = 6(x-8)

We'll remove the brackets:

y + 8 = 6x - 48

But x = 3y/4

y + 8 = 6*3y/4 - 48

y + 8 = 9y/2 - 48

We'll multiply by 2 all over:

2y + 16 = 9y - 96

We'll move the terms in y to the left side:

2y - 9y = -96 - 16

-7y = -112

We'll divide by -7:

y = 16

We'll come back into the expression of x:

x = 3*16/4

x = 3*4

x = 12

**The numbers are: x = 12 and y = 16.**