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 逆 of 3/7 . What is the fraction.

解

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}

解答ステップ

Represent the numbers with

x

numerator : x

denominator : 2 x + 4

A.T.Q.:

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

x

を解く

\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}