Question

There are nine water bottles in Devon’s refrigerator. He has three full boxes of water bottles to the refrigerator. Then he adds two more boxes that each has one fewer bottle than a full box when he is done there were 67 bottles in the refrigerator right and solve an equation to find the number of bottles in a full box.

Answer 1

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

According to the problem:

1. Devon starts with 9 water bottles in the refrigerator.
2. He adds 3 full boxes, which have \( 3x \) bottles.
3. He also adds 2 more boxes, where each box has one fewer bottle than a full box. Therefore, each of these boxes contains \( x - 1 \) bottles, leading to \( 2(x - 1) \) bottles from the two boxes.

Now we can sum these quantities to express the total number of bottles in the refrigerator:

\[
\text{Total bottles} = 9 + 3x + 2(x - 1)
\]

We are given that the total number of bottles after adding everything is 67:

\[
9 + 3x + 2(x - 1) = 67
\]

Now, let's simplify the equation:

1. Distribute the \( 2 \) in the term \( 2(x - 1) \):

\[
9 + 3x + 2x - 2 = 67
\]

2. Combine like terms:

\[
(3x + 2x) + (9 - 2) = 67
\]
\[
5x + 7 = 67
\]

3. Subtract 7 from both sides:

\[
5x = 67 - 7
\]
\[
5x = 60
\]

4. Divide both sides by 5:

\[
x = \frac{60}{5} = 12
\]

Thus, the number of bottles in a full box is \( \boxed{12} \).