The denominator of a certain fraction exceeds twice the numerator by 4. If the numerator is increased by 14 and the denominator is decreased by 9, the value of the resulting fraction is the multiplicative inverse of 3/7 . What is the fraction.

Solution

T h e d e n o mina t or o f a cer t ain f r a c t i o n e x cee d s tw i ce t h e n u m er a t or b y 4. I f t h e n u m er a t or i s in cre a se d b y 14 an d t h e d e n o mina t or i s d ecre a se d b y 9, t h e v a l u e o f t h e res u lt in g f r a c t i o n i s t h e m u lt i pl i c a t i v e in v erse o f \frac{3}{7} . Wha t i s t h e f r a c t i o n .

The number : \frac{113}{222}

Solution steps

Represent the numbers with

x

numerator : x

denominator : 2 x + 4

A.T.Q.:

\frac{x + 14}{2 x + 4 - 9} = \frac{3}{7}

Solve for

x, \frac{x + 14}{2 x + 4 - 9} = \frac{3}{7} : x = - 113

\frac{x}{2 x + 4} = \frac{- 113}{2 ( - 113 ) + 4} = \frac{113}{222}

The number : \frac{113}{222}