The sum of three consecutive even integers is 384 . What is the smallest of these integers?

Let's call the smallest integer \( x \). The next two consecutive even integers would then be \( x + 2 \) and \( x + 4 \). Adding these together gives us: \[ x + (x + 2) + (x + 4) = 384 \] This simplifies to: \[ 3x + 6 = 384 \] Subtracting 6 from both sides results in: \[ 3x = 378 \] Dividing both sides by 3 gives: \[ x = 126 \] So, the smallest of the three consecutive even integers is \( 126 \). An easy way to check your work is to quickly recalculate the integers: 126, 128, and 130, and add them—voilà, you get 384! It's always helpful to verify your answers in a fun way, just like solving a puzzle.