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 by 2 find the rational number

Answer 1

hii!!

here's ur answer...

let the numerator of the rational number be x.

therefore the denominator is x + 8

if the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2

==> ( x + 17 ) / ( x + 8 - 1 ) = 3/2

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

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

==> 2x + 34 = 3x + 21

==> 34 - 21 = 3x - 2x

==> 13 = x

==> x = 13

hence, numerator = x = 13 and denominator = x + 8 = 13 + 8 = 21

FINAL ANSWER = 13/21

hope this helps..!!

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