12. The sum of FOUR consecutive odd integers is 312 . What are the numbers? Introduce your variable, create an equation, then solve.

Let's introduce the variable to represent the first of the four consecutive odd integers. We'll call it \( x \). The next three odd integers can be expressed as \( x + 2 \), \( x + 4 \), and \( x + 6 \). The equation for their sum will look like this: \[ x + (x + 2) + (x + 4) + (x + 6) = 312 \] Combining like terms, we get: \[ 4x + 12 = 312 \] Next, we subtract 12 from both sides: \[ 4x = 300 \] Now, divide by 4: \[ x = 75 \] Thus, the four consecutive odd integers are: 75, 77, 79, and 81. Feeling accomplished? Well, the beauty of odd integers is that they end up being surprisingly simple to work with once you know how to set them up! Plus, they pop up in various contexts, from sequences in math to everyday problems involving even distribution or pairing!