What three consecutive integers have a sum of 822?

Here we will use algebra to find three consecutive integers whose sum is 822. 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 822. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 822

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 = 822
3X + 3 = 822

3X + 3 - 3 = 822 - 3
3X = 819

3X/3 = 819/3
X = 273

Which means that the first number is 273, the second number is 273 + 1 and the third number is 273 + 2. Therefore, three consecutive integers that add up to 822 are 273, 274, and 275.

273 + 274 + 275 = 822

We know our answer is correct because 273 + 274 + 275 equals 822 as displayed above.

Three Consecutive Integers
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What three consecutive integers have a sum of 823?
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