Question

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"? (Hint: cross products)

Answer 1

let the required fraction be \[\frac{ x }{ x+7 }\]
if the numerator is increased by 3,
then \[\frac{ x+3 }{ x+7 }=\frac{ 3 }{ 4 }\]
by cross multiplication we get,
4 ( x +3) = 3 (x+7)
4x+12=3x+21
4x-3x=21-12
x=9

So the required fraction is 9 / 16