Write an equation and solve to find the numbers and show work.
6. Find three consecutive even integers whose sum is 84.
Let x be the smallest even integer, then the next two consecutive even integers would be (x+2) and (x+4)
The sum of these three integers is 84, so we can write an equation:
x + (x+2) + (x+4) = 84
Simplifying and solving for x:
3x + 6 = 84
3x = 78
x = 26
So the smallest even integer is 26, and the next two consecutive even integers are:
(x+2) = 28
(x+4) = 30
Therefore, the three consecutive even integers are: 26, 28, 30.