Final answer:
The smallest even number is 75% of the largest among three consecutive even numbers. By setting up an equation and solving for the smallest number, we find it to be 12, with the following two numbers being 14 and 16. The sum of these three numbers is 42.
Step-by-step explanation:
The question poses a classic percentage and sequence problem that can be solved using algebra. We are looking for three consecutive even numbers where the smallest is 75% of the largest. We can define the smallest number as 'x', and because we are looking for even numbers, the next two numbers will be 'x + 2' and 'x + 4'. The condition given in the problem is that x = 0.75(x + 4).
To find x, we solve the equation:
x = 0.75(x + 4)
x = 0.75x + 3
x - 0.75x = 3
0.25x = 3
x = 3 / 0.25
x = 12. So, the smallest even number is 12, and the next two numbers are 14 and 16.
To find the sum of these three numbers, we add them together:
Sum = 12 + 14 + 16 = 42.
Therefore, the sum of the three even numbers is 42.