Question

sum of numerator and denominator of a fraction is equal to 7 .Four times numerator is 8 less than 5 times the denominator find the fraction​

Answer 1

Answer:

$\large{\boxed{\sf \dfrac{3}{4}}}$

Step-by-step explanation:

Let the numerator of the fraction be x and the denominator be y.

∴ Original fraction = $\dfrac{x}{y}$

Given that :

Sum of numerator and denominator is 7.

⇒ x + y = 7 .....(i)

Also,

Four times numerator is 8 less than 5 times the denominator.

⇒ 4x = 5y - 8

⇒ 4x - 5y = - 8 ....(ii)

Here, we got two equations. In order to get solution, multiply equation (i) by 4.

4(x + y) = 4 * 7

⇒ 4x + 4y = 28 ... (iii)

Subtracting eqⁿ (ii) from (iii) -

4x + 4y - (4x - 5y) = 28 - (-8)

⇒ 4x + 4y - 4x + 5y = 28 + 8

⇒ 9y = 36

⇒ y = $\dfrac{36}{9}$

⇒ y = 4

Substituting the value of y in (i) -

⇒ x + y = 7

⇒ x + 4 = 7

⇒ x = 7 - 4

⇒ x = 3

Hence, the required fraction is $\bf \dfrac{3}{4}.$