If the first and third of three odd consecutive integers are added, the result is 87 less than five times the second integer. Find the third integer.**Solution**

Let 2n + 1 be the first odd integer

Let 2n + 3 be the second odd integer

Let 2n + 5 be the third odd integer

Adding the first and the third gives the following expression.

2n + 1 + 2n + 5

87 less than five times the second integer gives the following expression.

5 × (2n + 3) - 87

If the first and third of three odd consecutive integers are added, the result is 87 less than five times the second integer.

The statement above gives the following equation

2n + 1 + 2n + 5 = 5 × (2n + 3) - 87

4n + 6 = 5 × 2n + 5 × 3 - 87

4n + 6 = 10n + 15 - 87

4n + 6 = 10n - 72

4n + 6 - 6 = 10n - 72 - 6

4n = 10n - 78

4n + 78 = 10n - 78 + 78

4n + 78 = 10n

4n - 4n + 78 = 10n - 4n

78 = 6n

Divide both sides by 6

78/6 = 6n/6

13 = n

The third integer is 2n + 5 or 2 × 13 + 5 = 26 + 5 = 31