Question

In a fraction 2 times the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator the new fraction is 2/3

Answer 1

Question:

In a fraction, 2 times the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator the new fraction is 2/3. Find the Orignal rational Number.

Answer:

Original Fraction = 7/12

Step-by-step explanation:

Let the Numerator = y

Denominator = 2y - 2

3 is added to the Numerator

⇒ Numerator = y + 3

⇒ Denominator = 2y - 2 + 3

⇒ 2y + 1

⇒ y + 3/2y + 1 = 2/3

⇒ 3 (y + 3) = 2 (2 y + 1)

⇒ 3y + 9 = 4y + 2

⇒ 3y - 4y = 2 - 9

⇒ -y = -7

⇒ y = 7

Numerator = y = 7

Denominator = 2y - 2

⇒ 2(7)-2

⇒ 14-2

⇒ 12

Original Fraction = 7/12