Question

The sum of 5 consecutive even integers is 430. Which integers are they?

Answer 1

Let's denote the five consecutive even integers as:

\[
x, \, x + 2, \, x + 4, \, x + 6, \, x + 8
\]

where \(x\) is the first even integer.

The sum of these integers can be expressed as:

\[
x + (x + 2) + (x + 4) + (x + 6) + (x + 8)
\]

Simplifying this, we have:

\[
5x + (2 + 4 + 6 + 8) = 5x + 20
\]

According to the problem, this sum equals 430:

\[
5x + 20 = 430
\]

To find \(x\), we first subtract 20 from both sides:

\[
5x = 410
\]

Now, we divide by 5:

\[
x = 82
\]

Now that we have \(x\), we can find the five consecutive even integers:

\[
82, \, 84, \, 86, \, 88, \, 90
\]

Thus, the five consecutive even integers are:

\[
\boxed{82, 84, 86, 88, 90}
\]