# How do you find three consecutive odd integers if three times the middle integer increased by the largest is 38?

May 16, 2017

The three consecutive odd integers are $7$, $9$ and $11$.

#### Explanation:

Let the three consecutive odd integers be $x$, $x + 2$ and $x + 4$.

As three times the middle number $x + 2$ is increased bt the largest i.e. $x + 4$, it becomes $3 \left(x + 2\right) + x + 4 = 3 x + 6 + x + 4 = 4 x + 10$.

Hence $4 x + 10 = 38$

i.e. $4 x = 38 - 10 = 28$ or $x = \frac{28}{4} = 7$

Hence the three consecutive odd integers are $7$, $9$ and $11$.