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.