Find three consecutive even integers whose sum is 66.

show work pls

three consecutive even integers are x, x+2 and x+4

x + x+2 + x+4 = 66
3x + 6 = 66
3x = 66-6
3x = 60
x = 60/3
x = 20  ← first integer

x + 2 = 20 + 2 = 22 ← second  integer

x + 4 = 20 + 4 = 24 ← third integer

For our three integers to be even x%2=0 ∀x∈S where S= {our three integers}. To guarantee this set our first integer as 2n (ie. 2n%n≡0). Then to have three consecutive even integers increment from the initial value by 2 thus setting them as 2n, 2n+2 and 2n+4.

Thus:


Simplifying:


Solving for 'n':



The integers are thus 2n=20, 2n+2=22 and 2n+4=24.

To check: 20+22+24=66.