Question

the denominator of a fraction is graeter than the numerator by 8 . if the numerator is increased by 17. and denominator is decreased by 1, the number obtained by 3/2. find the fraction​

Answer 1

Given :-

• The denominator of a fraction is graeter than the numerator by 8 . If the numerator is increased by 17 and denominator is decreased by 1, the number obtained by 3/2.

To find :-

• Required fraction

Solution :-

Let the numerator of fraction be x

• The denominator of a fraction is graeter than the numerator by 8.

• Denominator = x + 8

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

According to the given condition

→ 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

Therefore ,

• x = 13

Hence,

• Required fraction = Numerator/denominator

• x/x + 8 = 13/13 + 8 = 13/21

Answer 2

GiveN :-

• The denominator of a fraction is graeter than the numerator by 8 . if the numerator is increased by 17. and denominator is decreased by 1, the number obtained by 3/2.

To FinD :-

• To Find the Fraction required

CalculaTioN :-

Let us take Numerator and Denominator considering them as Variables and then with the given Conditions, the answer can be obtained.

• Let Numerator be x

The Dinominator of the Fraction is greater than 8

• So, denominator = x + 8

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

According to The Given conditions.

• x + 17/x + 8 - 1 = 3/2

• x + 17/x + 7 = 3/2

• 2(x + 17) = 3(x + 7)

• 2x + 34 = 3x + 21

Now, Making like terms to group it

• 34 - 21 = 3x - 2x

• x = 13

★ Numerator = 13

★ Denominator = 13 + 8 = 21

$\boxed{ \bf{ \red{hence \: x = 13 \: and \: fraction = \frac{13}{21} }{} }{} }{}$