Three consecutive even integers sum to 252. Which integers are they?

Answer 1

Let's denote the three consecutive even integers as \( x \), \( x + 2 \), and \( x + 4 \), where \( x \) is the first even integer.

According to the problem, the sum of these integers is 252:

\[ x + (x + 2) + (x + 4) = 252 \]

Now, we can simplify this equation:

\[ 3x + 6 = 252 \]

Next, we will isolate \( x \). Start by subtracting 6 from both sides:

\[ 3x = 252 - 6 \] \[ 3x = 246 \]

Now, divide both sides by 3:

\[ x = \frac{246}{3} \] \[ x = 82 \]

Now that we have the first even integer \( x = 82 \), we can find the other two integers:

1. The first integer: \( x = 82 \)
2. The second integer: \( x + 2 = 84 \)
3. The third integer: \( x + 4 = 86 \)

Thus, the three consecutive even integers are:

\[ \boxed{82}, \boxed{84}, \text{ and } \boxed{86} \]

To confirm, we can check their sum:

\[ 82 + 84 + 86 = 252 \]

This is correct, verifying that the integers are indeed 82, 84, and 86.