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Popular Word Problems >

The denominator of a fraction is three more than twice the numerator. If both numerator and denominator are decreased by one, the simplified result is 7/16 . Find the original fraction.

Solution

T h e d e n o mina t or o f a f r a c t i o n i s t h ree m ore t han tw i ce t h e n u m er a t or . I f b o t h n u m er a t or an d d e n o mina t or a re d ecre a se d b y o n e, t h e s im pl i f i e d res u lt i s \frac{7}{16} . F in d t h e or i g ina l f r a c t i o n .

Solution

The number : \frac{15}{33}

Solution steps

Represent the numbers with

x

:

numerator : x

denominator : 3 + 2 x

A.T.Q.:

\frac{x - 1}{3 + 2 x - 1} = \frac{7}{16}

Solve for

x, \frac{x - 1}{3 + 2 x - 1} = \frac{7}{16} : x = 15

\frac{x}{3 + 2 x} = \frac{15}{3 + 2 \cdot 15} = \frac{15}{33}

The number : \frac{15}{33}

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