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

Let us assume, x is the numerator and y is the denominator of the fraction x / y
Given:
y = x + 8
y - x = 8---------1
Also Given
x + 17/ y - 1 = 3/2
2 (x + 17) = 3 (y - 1)
2x + 34 = 3y -3
3y - 2x = 37 -----------2
Multiplying equation 1 by 3
3y - 3x = 24 ----------3
Subtract equation 3 from 1
x = 13
Therefore, y = x + 8 = 13 + 8 = 21
Therefore, the rational number = 13/21

Answer 2

Answer:

13/21

Step-by-step explanation:

1. Numerator = x
2. Denominator = x+ 8

x/x+8

• If the numerator is increased by 17

x + 17

• The denominator is decreased by 1

x + 8 - 1

x+17/x+7 = 3/2

• Cross multiplication used now

3(x + 7) = 2(x + 17)

3x + 21 = 2x + 34

3x - 2x = 34 - 21

x = 13

x/x + 8 = 13/13 + 8

13/21