What three consecutive integers have a sum of 563?

Here we will use algebra to find three consecutive integers whose sum is 563. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 563. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 563

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 563
3X + 3 = 563

3X + 3 - 3 = 563 - 3
3X = 560

3X/3 = 560/3
X = 186 2/3

Since 186 2/3 is not an integer, there is no true answer to this problem.

However, there are three numbers that add up to 563. The first number is (186 2/3), the second number is (186 2/3) + 1, and the third number is (186 2/3) + 2. Therefore, we could make this the answer to "Three consecutive numbers that add up to 563 are?":

186 2/3 + 187 2/3 + 188 2/3 = 563

Three Consecutive Integers
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What three consecutive integers have a sum of 564?
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