Question

The denominator of a fraction is 3 more than the numerator. If 5 is added to both numerator and denominator the resulting fraction becomes 4/5.  ​

Answer 1

Correct Question :

The denominator of a fraction is 3 more than the numerator. If 5 is added to both numerator and denominator the resulting fraction becomes 4/5.  Find the fraction.

Answer:

$\sf{The \:fraction \: is \: \frac{7}{10}}$

Step-by-step explanation:

Let,

The numerator of a fraction = x

The denominator of a fraction = x + 3

If 5 is added to both numerator and

denominator :

The numerator of a fraction = x + 5

The denominator of a fraction = x + 3 + 5

⇒ x + 3 + 5

⇒ x + 8

⇒ $\sf{\dfrac{x \: + \: 5}{x \: + \: 8 } \: = \: \dfrac{4}{5}}$

⇒ 5 (x + 5) = 4 (x + 8)

⇒ 5x + 25 = 4x + 32

⇒ 5x - 4x = 32 - 25

⇒ 1x = 7

⇒ x = 7

The numerator of a fraction = 7

The denominator of a fraction = x + 3

⇒ x + 3

⇒ 7 + 3

⇒ 10

The denominator of a fraction = 10

Therefore,

The fraction is $\sf{\dfrac{7}{10}}$

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The denominator of a fraction is 3 more than the numerator.

• If 5 is added to both the numerator and denominator the fraction becomes ⅘.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The fraction.

$\bf{\underline{\underline\green{Solution:-}}}$

According to the 1st condition:-

The denominator of a fraction is 3 more than the numerator.

Let the numerator be x

The denominator = x + 3

According to the 2nd condition:-

If 5 is added to both the numerator and denominator the fraction becomes ⅘.

If 5 is added to the numerator

The numerator = x + 5

If 5 is added to the denominator

The denominator = (x + 3) + 5 = (x + 8)

The fraction becomes ⅘

$\rm \implies \dfrac{x + 5}{x + 8} = \dfrac{4}{5}$

By cross multiplication:-

$\rm \implies {5(x + 5)} = {4(x + 8)}$

$\rm \implies {5x + 25} = {4x + 32}$

$\rm \implies {5x - 4x} = { 32 - 25}$

$\rm \implies {x} = { 7}$

The numerator = x = 7

The denominator

= x + 3

= 7 + 3

= 10

$\underline{\boxed{\rm \therefore The \: fration \: \: = \frac{7}{10} }}$