SOLUTION: Find three consecutive odd integers whose sum is 111. Are there three consecutive odd integers whose sum is 1111? Explain

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Question 459473: Find three consecutive odd integers whose sum is 111. Are there three consecutive odd integers whose sum is 1111? Explain
Answer by richard1234(5390) About Me  (Show Source):
You can put this solution on YOUR website!
We could let x-2, x, x+2 be the integers that sum up to 111 (x is an odd integer), so

(x-2) + x + (x+2) = 111

3x = 111 --> x = 37

There are no three consecutive odd integers that sum to 1111. From the previous example we got 3x = 111. 111 is a multiple of 3 so this works out. However, 1111 is not a multiple of 3, so this would imply that x is not an integer, contradiction.