Question

Find three consecutive odd integers whose sum is 489

Answer 1

161, 163, 165

Explanation:

x + x+2 + x +4 =489.

This is how we calculate three consecutive odd integers!

Combine like terms:

3x+6=489

3x=483

x=161

Three numbers are:

161, 161+2, 161+4.

161, 163, 165

Answer 2

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.