Answer:
162, 163, and 164.
Explanation:
Here we will use algebra to find three consecutive integers whose sum is 489. 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 489. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 489
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 = 489
3X + 3 = 489
3X + 3 - 3 = 489 - 3
3X = 486
3X/3 = 486/3
X = 162
Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.
162 + 163 + 164 = 489
We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.