Question

the denominator of the rational number is greater than is numerator by 8 if the numerator is increased by 17 and denominator is decreases by 1 .the number obtained is 3/2. find the rational number​

Answer 1

Step-by-step explanation:

Consider the numerator as x and denominator as y.

==> y = x + 8 ----- (As denominator of the rational number is greater than is numerator by 8)

==> (x + 17)/(y - 1) = 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

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

==> -x = -13

==> x = 13

Numerator = 13

Denominator = y

==> y = x + 8

==> y = 13 + 8

==> y = 21

x/y = 13/21

Hence, the rational number is 13/21.

Answer 2

Step-by-step explanation:

let the numerator be x

and

Denomenator be x + 8

GIVEN

X + 17 = 3

X+8 -- 1 2

CROSS MULTIPLY

2( X + 17 ) = 3 ( X+8 -- 1 )

2X + 34 = 3X + 24 -- 3

2X+ 34 = 3X + 21

34 - 21 = 3x -- 2x

13 = x

SO NUMERATOR = x = 13

AND

DENOMINATOR = X + 8 = 13 + 8 = 21