Question

Three consecutive integers have a sum of 21. What are the integers?

Answer 1

Let the three consecutive integers be \( x \), \( x + 1 \), and \( x + 2 \).

The sum of these integers can be expressed as:

\[
x + (x + 1) + (x + 2) = 21
\]

Simplifying the left-hand side:

\[
3x + 3 = 21
\]

Next, we subtract 3 from both sides:

\[
3x = 21 - 3
\]
\[
3x = 18
\]

Now, we divide both sides by 3:

\[
x = 6
\]

Thus, the three consecutive integers are:

\[
x = 6, \quad x + 1 = 7, \quad x + 2 = 8
\]

Therefore, the three consecutive integers are \( 6, 7, \) and \( 8 \).