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

1 answer

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:

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