SOLUTION: The sum of three consecutive odd integers is equal to the sum of two times the largest integer and seventy-seven. Find the numbers.

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Question 536873: The sum of three consecutive odd integers is equal to the sum of two times the largest integer and seventy-seven. Find the numbers.
Answer by fcabanski(1391) About Me  (Show Source):
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Three consecutive odd integers are n, n+2 and n+4


For example 1, 3, and 5. Note there is a difference of 2 between each consecutive odd integer.


Sum1: Their sum is n+n+2+n+4 = 3n+6


The largest integer is n+4 and 2 times the largest integer is 2*(n+4) = 2n+8.


Sum2: The sum of 2n+8 and 77 is 2n+8+77=2n+85.


Now we have both sides. Sum1=Sum2:


3n + 6 = 2n + 85


Subtract 2n from both sides, and subtract 6 from both sides.


n=79.


The consecutive integers are 79, 81, and 83.

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