The local deli charges a fee for delivery. On Monday, they delivered two dozen bagels to an office at a total cost of $8. On Tuesday, three dozen bagels were delivered at a total cost of $11. Which system of equations could be used to find the cost of a dozen bagels, b, if the delivery fee is f?

Options

A. `b+2f=8`
`b+3f=11`
B. `2b+f=8`
`b+3f=11`
C. `b+2f=8`
`3b+f=11`
D. `2b+f=8`
`3b+f=11`

Answer

To solve the problem, we need to set up a system of equations based on the information given about the deliveries of bagels and their costs.

1. **Define the Variables**:
- Let \( b \) be the cost of a dozen bagels.
- Let \( f \) be the delivery fee.

2. **Set Up the Equations**:
- From Monday's delivery, we know that 2 dozen bagels were delivered for a total cost of $8. This can be expressed as:
\[ 2b + f = 8 \]
- From Tuesday's delivery, 3 dozen bagels were delivered for a total cost of $11. This can be expressed as:
\[ 3b + f = 11 \]

3. **Write the System of Equations**:
- We now have the following system of equations:
\[ \begin{align*} 2b + f &= 8 \quad \text{(1)} \\ 3b + f &= 11 \quad \text{(2)} \end{align*} \]

4. **Conclusion**:
- The system of equations that can be used to find the cost of a dozen bagels \( b \) and the delivery fee \( f \) is:
\[ \begin{align*} 2b + f &= 8 \\ 3b + f &= 11 \end{align*} \]