40. Make Sense and Persevere There are nine water bottles in Devin's refrigerator. He adds three full boxes of water bottles to the refrigerator. Then he adds two more boxes that each have 1 fewer bottle than a full box. When he is done, there are 67 bottles in the refrigerator. Write and solveran equation to find the number of bottles in a full box. (C MP.

Let's denote the number of bottles in a full box as \( x \). 1. **Initial Bottles**: Devin starts with 9 water bottles in the refrigerator. 2. **Full Boxes Added**: He adds 3 full boxes of water bottles, which means he adds \( 3x \) bottles. 3. **Additional Boxes**: He then adds 2 more boxes, each containing 1 fewer bottle than a full box. Therefore, each of these boxes contains \( x - 1 \) bottles. Since he adds 2 of these boxes, he adds \( 2(x - 1) \) bottles. Now, we can set up the equation based on the total number of bottles in the refrigerator after all additions: \[ 9 + 3x + 2(x - 1) = 67 \] Now, let's simplify and solve the equation: 1. Distribute the \( 2 \) in the equation: \[ 9 + 3x + 2x - 2 = 67 \] 2. Combine like terms: \[ 9 - 2 + 3x + 2x = 67 \] \[ 7 + 5x = 67 \] 3. Subtract 7 from both sides: \[ 5x = 67 - 7 \] \[ 5x = 60 \] 4. Divide by 5: \[ x = \frac{60}{5} \] \[ x = 12 \] Thus, the number of bottles in a full box is \( \boxed{12} \).