Answer: The three consecutive even numbers are 22, 24, 26
22+24+26 = 72
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Step-by-step explanation:
- x = first even number
- x+2 = second even number directly right after x
- (x+2)+2 = x+4 = third even number directly after x+2
For example, if x = 12, then we'd have x+2 = 12+2 = 14 and x+4 = 14+4 = 18.
However 12+14+18 = 44 is not 72 like we want.
You can guess-and-check your way to the answer, but a faster efficient route is to use algebra. Add up those x expressions and set the sum equal to 72 and solve.
(first) + (second) + (third) = 72
(x) + (x+2) + (x+4) = 72
3x+6 = 72
3x = 72-6
3x = 66
x = 66/3
x = 22
So we have,
- x = 22 = first even number
- x+2 = 22+2 = 24 = second even number
- x+4 = 22+4 = 26 = third even number
As a check: 22+24+26 = 72 which verifies the answers.