Question

the sum of the numerator and denominator of a fraction is 3 less than the twice the denominator . If the numerator and the denominator are decreased by 1, the numerator becomes half the denominator determine the fraction

Answer 1

Let the numerator be x and the denominator be y.
Given that the sum of numerator and denominator is 3 less than twice the denominator
x + y = 2y - 3
x - y = - 3(Equation 1)

And also given that if the numerator and denominator are decreased by 1, the numerator becomes half of the denominator.
2(x - 1) = y - 1
2x - 2 = y - 1
2x - y = 1(Equation 2)

By Subtracting equation 2 from 1
x - y = - 3
- 2x + y = - 1

- x = - 4
x = 4
Therefore
4 - y = - 3
y = 7

Therefore the fraction is x/y is 4/7