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the sum of three consecutive odd integers such that seven times the sum of the first two integers is three more than nine times the third integer

Solution

the sum of three consecutive odd integers such that seven times the sum of the first two integers is three more than nine times the third integer

Solution

The numbers : - 5 \frac{2}{7}, - 3 \frac{2}{7}, - 1 \frac{2}{7}

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number 1 : x + 2

Consecutive number 2 : x + 4

A.T.Q.:

x + x + 2 = 3 + 9 (x + 4)

Solve

x + x + 2 = 3 + 9 (x + 4) : x = - \frac{37}{7}

x + 2 = - \frac{37}{7} + 2 = - \frac{23}{7}

x + 4 = - \frac{37}{7} + 4 = - \frac{9}{7}

Convert improper fractions to mixed numbers:

\frac{37}{7} = 5 \frac{2}{7}

Convert improper fractions to mixed numbers:

\frac{23}{7} = 3 \frac{2}{7}

Convert improper fractions to mixed numbers:

\frac{9}{7} = 1 \frac{2}{7}

The numbers : - 5 \frac{2}{7}, - 3 \frac{2}{7}, - 1 \frac{2}{7}

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