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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Apr 24, 23 07:02 AM