The sum of three consecutive integers is 105. What are the three integers?

34, 35, 36

Step-by-step explanation:

34 + 35 + 36 = 105

34

35

36

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 105.

We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third 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 3 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 third number is 34+2. Therefore, three consecutive integers that add up to 105 are:

34

35

36