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Popular Word Problems >

The sum of the reciprocals of 2 consecutive integers is 23/132 . Find the numbers

Solution

T h e s u m o f t h e rec i p roc a l s o f 2 co n sec u t i v e in t e g ers i s 23/132 . F in d t h e n u mb ers

Solution

The numbers : 11, 12 or - \frac{12}{23}, \frac{11}{23}

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number : x + 1

A.T.Q.:

\frac{1}{x} + \frac{1}{x + 1} = \frac{23}{132}

Solve

\frac{1}{x} + \frac{1}{x + 1} = \frac{23}{132} : x = 11, x = - \frac{12}{23}

Plug in

x = 11 : 12

Plug in

x = - \frac{12}{23} : \frac{11}{23}

The numbers : 11, 12 or - \frac{12}{23}, \frac{11}{23}

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