Question

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

Answer 1

Answer:

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Step-by-step explanation:

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be x/x + 8.

According to the given cndition,

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

=x=13

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = 13/21

Answer 2

Given :-

• 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

To find :-

• Required number

Solution :-

Let the numerator be x then denominator be (x + 8)

• It is given that numerator is increased by 17 and the denominator is decreased by 1.

• Number obtained is 3/2.

According to the given condition

→ x + 17/(x + 8) - 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

→ 34 - 21 = 3x - 2x

→ x = 13

Hence,

• Required number = Numerator/Denominator

• x/x + 8 = 13/13 + 8 = 13/21