Question

The numerator of a fraction is 4 less than the denominator. If 3 is subtracted from
ne numerator and 1 is added to the denominator, the new fraction becomes1by 5
Find the original system​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let the denominator be x.

So,

Numerator = x - 4 __ (eq 1)

According to question

If 3 is subtracted from the numerator and 1 is added to the denominator, the new fraction becomes 1/5.

Now,

Numerator = x - 4 - 3 => x - 7

Denomination = x + 1

⇒ $\sf{\frac{x\:-\:7}{x\:+\:1}\:=\:\frac{1}{5}}$

Cross-multiply them

⇒ $\sf{5(x\:-\:7)\:=\:1(x\:+\:1)}$

⇒ $\sf{5x\:-\:35\:=\:x\:+\:1}$

⇒ $\sf{5x\:-\:x\:=\:1\:+\:35}$

⇒ $\sf{4x\:=\:36}$

⇒ $\sf{x\:=\:9}$

Substitute value of x = 9 in (eq 1)

⇒ Numerator = 9 - 4

⇒ Numerator = 5

And

⇒ Denominator = 9

•°• Fraction = $\sf{\frac{Numerator}{Denominator}}$

⇒ $\sf{\frac{5}{9}}$