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. Find the rational number.​

Answer 1

Correct 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.

Given :-

• The denominator of a rational number is greater than its numerator by 8.

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

To Find :-

• What's the rational number?

Solution :-

Let the numerator of the given rational number be x.

Given that,

The denominator of a rational number is greater than its numerator by 8.

That's why,

Denominator = x +8

Again, it's given that __

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

According to the question :-

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

⟼ ( x +17) / ( x+7) =3/2

⟼ 2( x +17) = 3 (x+7)

⟼2x + 34 = 3x + 21

⟼ 3x -2x = 34 -21

$⟼x = 13$

Hence,

the numerator of the given rational number is =13

Denominator = x +8 = 13 + 8 = 21

Therefore, rational number = 13/21

Answer 2

Answer:

Correct 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.

Given :-

• The denominator of a rational number is greater than its numerator by 8.

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

To Find :-

• What's the rational number?

Solution :-

Let the numerator of the given rational number be x.

Given that,

The denominator of a rational number is greater than its numerator by 8.

That's why,

Denominator = x +8

Again, it's given that __

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

According to the question :-

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

⟼ ( x +17) / ( x+7) =3/2

⟼ 2( x +17) = 3 (x+7)

⟼2x + 34 = 3x + 21

⟼ 3x -2x = 34 -21

⟼x = 13⟼x=13

Hence,

the numerator of the given rational number is =13

Denominator = x +8 = 13 + 8 = 21

Therefore, rational number = 13/21