Here we will use algebra to find three consecutive integers whose sum is 228. 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 228. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 228
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 = 228
3X + 3 = 228
3X + 3 - 3 = 228 - 3
3X = 225
3X/3 = 225/3
X = 75
Which means that the first number is 75, the second number is 75 + 1 and the third number is 75 + 2. Therefore, three consecutive integers that add up to 228 are 75, 76, and 77.
75 + 76 + 77 = 228
We know our answer is correct because 75 + 76 + 77 equals 228 as displayed above.
