Question

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

Answer 1

Step-by-step explanation:

Let the numerator and denominator be x and y respectively

$x - y = 8 \\ x = 8 + y\: \: \: \: \: \: (1) \\ \\ \frac{x + 17}{y - 1} = \frac{3}{2} \\ \\ 2x + 34 = 3y - 3 \\ 3y - 2x = 37 \: \: \: \: \: \: \: (2) \\ \\ from \: 1 \: and \: 2 \\ \\ 3y - 2(8 + y) = 37 \\ 3y - 16 - 2y = 37 \\ y = 37 + 16 = 53 \: \: \: \: \: (3) \\ \\ from \: (1) \: \: and \: \: (3) \\ x = 8 + 53 = 61$

rational number = 61/53