What three consecutive integers have a sum of 825?

Here we will use algebra to find three consecutive integers whose sum is 825. 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 825. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 825

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 = 825
3X + 3 = 825

3X + 3 - 3 = 825 - 3
3X = 822

3X/3 = 822/3
X = 274

Which means that the first number is 274, the second number is 274 + 1 and the third number is 274 + 2. Therefore, three consecutive integers that add up to 825 are 274, 275, and 276.

274 + 275 + 276 = 825

We know our answer is correct because 274 + 275 + 276 equals 825 as displayed above.

Three Consecutive Integers
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What three consecutive integers have a sum of 826?
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