What three consecutive integers have a sum of 1683?

Here we will use algebra to find three consecutive integers whose sum is 1683. 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 1683. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 1683

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 = 1683
3X + 3 = 1683

3X + 3 - 3 = 1683 - 3
3X = 1680

3X/3 = 1680/3
X = 560

Which means that the first number is 560, the second number is 560 + 1 and the third number is 560 + 2. Therefore, three consecutive integers that add up to 1683 are 560, 561, and 562.

560 + 561 + 562 = 1683

We know our answer is correct because 560 + 561 + 562 equals 1683 as displayed above.

Three Consecutive Integers
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What three consecutive integers have a sum of 1684?
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