Let's solve the problem step by step.
### Problem
The sum of 3 consecutive even numbers is 108. What are the numbers?
### Step-by-Step Solution
1. Define the numbers:
Let the first number be [tex]\(2k\)[/tex], where [tex]\(k\)[/tex] is an integer.
Since the numbers are consecutive and even:
- The second number is [tex]\(2k + 2\)[/tex]
- The third number is [tex]\(2k + 4\)[/tex]
2. Write the equation based on the given sum:
[tex]\[
(2k) + (2k + 2) + (2k + 4) = 108
\][/tex]
3. Simplify the equation:
Combine the terms:
[tex]\[
2k + 2k + 2 + 2k + 4 = 108
\][/tex]
[tex]\[
6k + 6 = 108
\][/tex]
4. Solve for [tex]\(k\)[/tex]:
Subtract 6 from both sides to isolate the term with [tex]\(k\)[/tex]:
[tex]\[
6k + 6 - 6 = 108 - 6
\][/tex]
[tex]\[
6k = 102
\][/tex]
Divide both sides by 6:
[tex]\[
k = \frac{102}{6}
\][/tex]
[tex]\[
k = 17
\][/tex]
5. Find the three consecutive even numbers:
Substitute [tex]\(k = 17\)[/tex] back into the expressions for the numbers:
- First number: [tex]\(2k = 2 \times 17 = 34\)[/tex]
- Second number: [tex]\(2k + 2 = 34 + 2 = 36\)[/tex]
- Third number: [tex]\(2k + 4 = 34 + 4 = 38\)[/tex]
### Conclusion
So the three consecutive even numbers whose sum is 108 are:
- 34, 36, and 38.
The largest of these numbers is 38.
