Question

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

Answer 1

Answer:

$\bf{\dfrac{3}{4}}$

Explanation:

Given

• Sum of numerator and denominator of a fraction is equal to 7
• Numerator is 8 less than 5 times of the denominator

To Find :

• We have to find fraction.

Solution :

Assume numerator as  “x” and denominator as “y”

ATQ

x+y=7..........(1)

5y-4x=8.......(2)

Multiply equation  (1) by 4

4x+4y=28......(3)

Add equation (3) and (2)

$\ \ \ 4y +4x = 28\\ +5y -4x = 08 \\- - - - - - - - \\\ \ \ \ \ \ \ {}{}{}{}\ \ \ 9y\ + \ 0=36\\- - - - - - - -$

So,

9y=20

y=36/9

y=4

Let’s put y in the equation that we made earlier

$\sf{}x + y = 7\\ \sf{}x + 4 = 7 \\ \sf{}x = 7 - 4\\ \sf{}x= 3$

Now we know both x and y,so the fraction form will be

$\rightarrow \dfrac{3}{4}$