What is the sum of three consecutive even integers if the sum of the first and third integers is $128$?
I need to find three consecutive even integers, so I can call them $x, x+2, x+4$, where $x$ is the smallest one. Then, the sum of the first and third integers is $x + (x+4) = 128$, according to the problem. I can simplify this equation by combining like terms: $2x + 4 = 128$. To isolate $x$, I can subtract $4$ from both sides: $2x = 124$. Then, I can divide both sides by $2$: $x = 62$. So, the smallest even integer is $62$, and the other two are $64$ and $66$. To find the sum of all three, I can add them up: $62 + 64 + 66 = 192$. 