What three consecutive integers have a sum of 105?

Here we will use algebra to find three consecutive integers whose sum is 105. 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 105. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 105

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 = 105
3X + 3 = 105

3X + 3 - 3 = 105 - 3
3X = 102

3X/3 = 102/3
X = 34

Which means that the first number is 34, the second number is 34 + 1 and the third number is 34 + 2. Therefore, three consecutive integers that add up to 105 are 34, 35, and 36.

34 + 35 + 36 = 105

We know our answer is correct because 34 + 35 + 36 equals 105 as displayed above.

Three Consecutive Integers
Enter another number below to find what three consecutive integers add up to its sum.

What three consecutive integers have a sum of 106?
Here is the next algebra problem we solved.