 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 has 1 fewer bottle than a full box. When he is​ done, there are 67 bottles in the refrigerator. Write and solve an equation to find the number of bottles in a full box.

Let's define the unknown quantity:

- Let \( x \) be the number of bottles in a full box.

### Step 1: Express the number of bottles added to the refrigerator.

1. **Three full boxes of bottles:**
   - Total number of bottles from three full boxes: \( 3x \).

2. **Two boxes with 1 fewer bottle than a full box:**
   - Each of these boxes has \( x - 1 \) bottles.
   - Total number of bottles from these two boxes: \( 2(x - 1) \).

### Step 2: Set up the equation.

- Devin starts with 9 water bottles in the refrigerator.
- He adds \( 3x \) bottles from the full boxes.
- He adds \( 2(x - 1) \) bottles from the boxes with 1 fewer bottle.
- The total number of bottles in the refrigerator is 67.

So, the equation is:
\[
9 + 3x + 2(x - 1) = 67
\]

### Step 3: Simplify and solve the equation.

1. Expand the equation:
   \[
   9 + 3x + 2x - 2 = 67
   \]

2. Combine like terms:
   \[
   5x + 7 = 67
   \]

3. Subtract 7 from both sides:
   \[
   5x = 60
   \]

4. Divide both sides by 5:
   \[
   x = 12
   \]

### Answer:

The number of bottles in a full box is **12**.

Would you like more details or have any questions?

Here are five related questions:

1. What if Devin had only 5 bottles in the refrigerator initially?
2. How many total bottles would Devin have if he added 4 full boxes instead?
3. How would the equation change if one of the boxes with fewer bottles had 2 fewer bottles instead of 1?
4. What if Devin adds another full box after adding the other boxes? How many bottles will he have then?
5. If the refrigerator can hold a maximum of 80 bottles, how many more bottles can he add?

**Tip:** When setting up equations, carefully define the unknown and write expressions for each part of the problem before combining them into the final equation.

Learn how to solve Devin's problem involving water bottles in his refrigerator. Follow a detailed step-by-step solution to find out how many bottles are in a full box. Suitable for students in Grades 7-9.

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