Question

Four consecutive even integers add up to 324. What is the least of these integers?

Answer 1

Let the four consecutive even integers be represented as \( x, x+2, x+4, x+6 \).

To find the sum of these integers, we can set up the equation:

\[
x + (x + 2) + (x + 4) + (x + 6) = 324
\]

Simplifying the left side, we combine like terms:

\[
4x + 12 = 324
\]

Next, we isolate \( x \) by subtracting 12 from both sides:

\[
4x = 324 - 12
\]
\[
4x = 312
\]

Now, divide both sides by 4:

\[
x = \frac{312}{4}
\]
\[
x = 78
\]

Thus, the four consecutive even integers are:

- \( x = 78 \)
- \( x + 2 = 80 \)
- \( x + 4 = 82 \)
- \( x + 6 = 84 \)

The least of these integers is \( x \), which is:

\[
\boxed{78}
\]