What three consecutive integers have a sum of 8123?

Here we will use algebra to find three consecutive integers whose sum is 8123. 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 8123. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 8123

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 = 8123
3X + 3 = 8123

3X + 3 - 3 = 8123 - 3
3X = 8120

3X/3 = 8120/3
X = 2706 2/3

Since 2706 2/3 is not an integer, there is no true answer to this problem.

However, there are three numbers that add up to 8123. The first number is (2706 2/3), the second number is (2706 2/3) + 1, and the third number is (2706 2/3) + 2. Therefore, we could make this the answer to "Three consecutive numbers that add up to 8123 are?":

2706 2/3 + 2707 2/3 + 2708 2/3 = 8123

Three Consecutive Integers
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What three consecutive integers have a sum of 8124?
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