Question
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.
Question content area bottom
Part 1
Write the equation.
enter your response here
(Type an equation using b as the variable. Do not simplify.
Question content area bottom
Part 1
Write the equation.
enter your response here
(Type an equation using b as the variable. Do not simplify.
Answers
GPT-4o mini
Let's denote \( b \) as the number of bottles in a full box.
Initially, Devin has 9 water bottles.
When he adds three full boxes of water bottles, he adds \( 3b \) bottles.
Then he adds two more boxes, each containing \( b - 1 \) bottles (since each has 1 fewer bottle than a full box). Therefore, he adds \( 2(b - 1) \) bottles from these two boxes.
Now we can write the equation for the total number of bottles in the refrigerator after all additions:
\[
9 + 3b + 2(b - 1) = 67
\]
This is the equation we need to solve to find the number of bottles in a full box \( b \).
Initially, Devin has 9 water bottles.
When he adds three full boxes of water bottles, he adds \( 3b \) bottles.
Then he adds two more boxes, each containing \( b - 1 \) bottles (since each has 1 fewer bottle than a full box). Therefore, he adds \( 2(b - 1) \) bottles from these two boxes.
Now we can write the equation for the total number of bottles in the refrigerator after all additions:
\[
9 + 3b + 2(b - 1) = 67
\]
This is the equation we need to solve to find the number of bottles in a full box \( b \).