Question

There are 3 consecutive even integers with a sum of 66. What are the integers?

Answer 1

To find three consecutive even integers that sum to 66, let's define the integers.

Let the first even integer be \( x \). Therefore, the next two consecutive even integers can be expressed as \( x + 2 \) and \( x + 4 \).

The equation for their sum will be:
\[
x + (x + 2) + (x + 4) = 66
\]

Simplifying this equation:
\[
x + x + 2 + x + 4 = 66
\]
\[
3x + 6 = 66
\]

Next, we can subtract 6 from both sides:
\[
3x = 60
\]

Now, divide by 3:
\[
x = 20
\]

Thus, the three consecutive even integers are:
\[
20, 22, \text{ and } 24
\]

So, the integers are **20, 22, and 24**.