# If the first and third of three consecutive odd integers are added, the result is 57 less than five times the second integer. How do you find the third integer?

May 9, 2017

The third integer is $21$

#### Explanation:

Let the three consecutive odd integers be $2 n - 1 , 2 n + 1 \mathmr{and} 2 n + 3$

By condition , $\left(2 n - 1\right) + \left(2 n + 3\right) = 5 \left(2 n + 1\right) - 57$ or

$2 n - 1 + 2 n + 3 = 10 n + 5 - 57 \mathmr{and} 4 n + 2 = 10 n - 52 \mathmr{and} 6 n = 54 \mathmr{and} n = 9$

Three consecutive odd integers are $2 n - 1 = 17 , 2 n + 1 = 19 \mathmr{and} 2 n + 3 = 21$

The third integer is $21$ [Ans]