The denominator of a fraction is 1 more then twice its numerator. if t

1.	The denominator of a fraction is 1 more then twice its numerator. if the numerator and denominator are both increased by 5, it becomes 3/5 . find the original fraction
Answer» Step-by-step EXPLANATION: Let, • The numerator of a fraction = x • The denominator of a fraction = 2x + 1 ★ If the numerator and denominator are both increased by 5, it becomes 3/5 • The numerator of a fraction = x + 5 • The denominator of a fraction = 2x + 1 + 5 = 2x + 6 ★ According to the Question : ⇒ $\dfrac{(x \: + \: 5) }{(2x \: + 6)} \: = \: \dfrac{3}{5}$ ⇒ 5 (x + 5) = 3 (2x + 6) ⇒ 5X + 25 = 6x + 18 ⇒ 5x - 6x = 18 - 25 ⇒ - x = - 7 ⇒ x = 7 The numerator of a fraction = 7 The denominator of a fraction = 2x + 1 ⇒ 2 (7) + 1 ⇒ 14 + 1 ⇒ 15 The denominator of a fraction = 15 Therefore, The original fraction is $\dfrac{7}{15}$

The denominator of a fraction is 1 more then twice its numerator. if the numerator and denominator are both increased by 5, it becomes 3/5 . find the original fraction

Answer»

Step-by-step EXPLANATION:

Let,

• The numerator of a fraction = x

• The denominator of a fraction = 2x + 1

★ If the numerator and denominator are both increased by 5, it becomes 3/5

• The numerator of a fraction = x + 5

• The denominator of a fraction = 2x + 1 + 5

= 2x + 6

★ According to the Question :

⇒ $\dfrac{(x \: + \: 5) }{(2x \: + 6)} \: = \: \dfrac{3}{5}$

⇒ 5 (x + 5) = 3 (2x + 6)

⇒ 5X + 25 = 6x + 18

⇒ 5x - 6x = 18 - 25

⇒ - x = - 7

⇒ x = 7

The numerator of a fraction = 7

The denominator of a fraction = 2x + 1

⇒ 2 (7) + 1

⇒ 14 + 1

⇒ 15

The denominator of a fraction = 15

Therefore, The original fraction is $\dfrac{7}{15}$