Final answer:
To find three consecutive even numbers whose sum is 618, we let the smallest number be n, and the sequence can be represented by n, n+2, and n+4. The numbers are found to be 204, 206, and 208.
Step-by-step explanation:
The question involves finding three consecutive even numbers whose sum is 618. To solve this, let's denote the smallest of these numbers as n. Since the numbers are consecutive even numbers, the next two numbers would be n+2 and n+4. The sum of these three numbers is given by n + (n+2) + (n+4) = 618.
Simplify the equation to get 3n + 6 = 618. Subtract 6 from both sides to get 3n = 612, then divide by 3 to find n = 204. Therefore, the three consecutive numbers are 204, 206, and 208.