We know that "consecutive" means next to each other.
Let's make "x" the first integer, x+1 the second, and x+2 the third. For example, we could make x = 1.
Then we can plug this into our equation:
x + (x+1) + (x+2) = 57.
1 + (1+1) + (1+2) = 57
1 + 2 + 3 = 57.
So as you can tell, this does NOT work.
Let's continue the original equation:
x + (x+1) + (x+2) = 57.
Combine like terms:
x + x + 1 + x + 2 = 57.
3x = 57 - 2 - 1.
3x = 54.
x = 18.
x + 1 = 19
x + 2 = 20.
Add these up for proof: 18 + 19 + 20 = 57
:)
