Answer:
34
35
36
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