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 invers of 3/7 . What is the fraction.

Lösung

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}

Schritte zur Lösung

Represent the numbers with

x

numerator : x

denominator : 2 x + 4

A.T.Q.:

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

Löse nach

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}