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

N+D=7
4N=5D-8
D=4
N=3
3/4

Answer 2

let fraction be x/y
given x+y = 7........eqn 1
        4x=5y-8
        that is 5y-4x=8..........eqn 2
to equate coef of y multiply eqn 1 by 5
           so 5(x + y = 7)
              =5x+5y=35.............eqn 3
sub eqn 2 from eqn 3
 =9x =27
x=3
 substituting value of x in eqn 1
x + y =7
 3+y=7 
y=4
so the fraction is 3/4