Melanie purchases 6 basketballs and 2 volleyballs for $114. A volleyball cost her $3 less than a basketball. How much did each volleyball cost?

Let's solve this step by step:

Step 1: Let's denote the cost of a basketball as B and the cost of a volleyball as V. We know from the problem that a volleyball costs $3 less than a basketball, so we can write this as: V = B - 3.

Step 2: We also know that Melanie spent $114 on 6 basketballs and 2 volleyballs. We can write this as: 6B + 2V = 114.

Step 3: Now we can substitute V from our first equation into our second equation. This gives us: 6B + 2(B - 3) = 114.

Step 4: Simplify the equation: 6B + 2B - 6 = 114.

Step 5: Combine like terms: 8B - 6 = 114.

Step 6: Add 6 to both sides of the equation: 8B = 120.

Step 7: Divide both sides by 8 to solve for B: B = 15. So, each basketball costs $15.

Step 8: Substitute B = 15 into the first equation to find the cost of each volleyball: V = 15 - 3 = 12. So, each volleyball costs $12.