Question

the denominator of a rational, number exceeds its numerator by 8 . if 7 is added
from the numerator as well as the denominator the value of the new rational number is 1/2 find the original rational numbers.

Answer 1

Answer:

12:48

Step-by-step explanation:

12:18

Explanation:

If we have 1:2 adding 1 to both the numerator and denominator the rational number is 2:3.

But 2:3 can’t be the final solution because the numerator + 6 is equal to the denominator. So both have to be multiplied by the same number. We could say that:

(2*x)+6 = 3*x;

Then

x=6;

And

(2*6):(3*6)=12:18

Answer 2

Answer:

$let \: the \: numerator \: x \\ then \: denominator \: = x + 8 \\ = \frac{x}{x + 8} atq \\ \frac{x + 7}{x + 8 + 7} = \frac{1}{2} \\ \frac{x + 7}{x + 15} = \frac{1}{2} \: \: \: (then \: by \: cross \: multiplying) \\( x + 7) \times 2 = 1 \times (x + 15) \\ 2x + 14 = x + 15 \\ = 2x - x = 15 - 14 \\ x = 1 \\ x + 8 = 1 + 8 = 9 \\ rational \: number = \frac{1}{9}$