Consecutive odd integers word problem

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

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