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

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

let the fraction will be `x/y`.
According to the question,
x + y = 7                                    ...(1)
5y - 4x = 8                                 ...(2)

Multiplying equation no. (1) by 4
4x + 4y = 28                              ...(3)
Adding equation (3) and (2)
     4x + 4y = 28
+ - 4x + 5y = 8  
              9y = 36
               y = 4

From (1),
x + 4 = 7
x = 3
Required fraction = `3/4`.