Question

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

Answer 1

numerator = x   denominator= y

1. x/x+8

2.x+17/x+8-1=3/2

x+17/x+7=3/2

(x+17)2= (x+7)3  [cross multiply]

2x+34 = 3x+21

34-21 = 3x-2x  ["x" on one side and constants on one side]

13 = x     [that is, 1x]

from eqn 1, x/x+8

x+8 = y = denominator

13+8 = y

21= y

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