Question

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

Answer 1

let the fraction be x/y
$x + y + 3 = 2y \\ x - y = - 3 \: \: \: \: \: eq1 \\ \frac{x - 1}{y - 1} = \frac{ \frac{y}{2} }{y} = \frac{1}{2} \\ 2x - 2 = y - 1 \\ 2x - y = 1 \: \: \: \: eq2 \\ subtract \: both \: eqs \\ - x = - 4 \\ x = 4 \\ 4 - y = - 3 \\ - y = - 3 - 4 = - 7 \\ y = 7 \\ so \: the \: fraction \: is \: \frac{4}{7}$