Question

7. The denominator of a fraction is 1 more than twice its numerator. If the numerator
and denominator are both increased by 5, it becomes
3
Find the original fraction.
Find two positive numbers in the no
5​

Answer 1

Step-by-step explanation:

Case 1:-

Let the numerator of the fraction be x

The denominator is 1 more than twice its numerator.

The denominator = 2x + 1

Case 2:-

If the numerator is increased by 5

The numerator becomes = x + 5

If the denominator is increased by 5

The denominator becomes 2x + 1 + 5 = 2x + 6

The fraction becomes 3/5

$\sf\dashrightarrow\dfrac{x + 5}{2x + 6} = \dfrac{3}{5}$

$\sf\dashrightarrow 5(x + 5) = 3(2x + 6)$

$\sf\dashrightarrow 5x + 25 = 6x + 18$

$\sf\dashrightarrow 6x - 5x = 25 - 18$

$\sf\dashrightarrow x = 7$

The numerator = x = 7

The denominator = 2x + 1 = 2(7) + 1 = 15

$\sf Fraction = \dfrac{Numerator}{Denominator}$

$\dashrightarrow \underline{\boxed{\sf \therefore The \: fraction = \dfrac{7}{15}}}$