Question

A set of 3 consecutive odd integers has a sum of 33. What are the integers?

Answer 1

Let the three consecutive odd integers be represented as \( x \), \( x + 2 \), and \( x + 4 \).

The sum of these integers can be expressed as:

\[
x + (x + 2) + (x + 4) = 33
\]

Combining the terms gives:

\[
3x + 6 = 33
\]

Next, we solve for \( x \) by subtracting 6 from both sides:

\[
3x = 33 - 6
\]
\[
3x = 27
\]

Now, divide both sides by 3:

\[
x = \frac{27}{3} = 9
\]

Now that we have \( x \), we can find the three consecutive odd integers:

- First integer: \( x = 9 \)
- Second integer: \( x + 2 = 11 \)
- Third integer: \( x + 4 = 13 \)

Thus, the three consecutive odd integers are:

\[
\boxed{9, 11, 13}
\]