Question

At their family's pizzeria, Jake and Alyssa were folding pizza boxes to get ready for the day. 

Jake can fold 8 boxes per minute and has already folded 10 boxes.

Alyssa can fold 6 boxes per minute and has already folded 20 boxes.

Which system of equations represents the number of boxes, b, that Jake and Alyssa will fold based on the minutes worked, m?

A. 

b=10m+8b=20m+6

B. 

b=8m+10b=6m+20

C. 

m=10b+8m=20b+6

D. 

Answer 1

To formulate the system of equations that represents the number of boxes, \( b \), that Jake and Alyssa will fold based on the minutes worked, \( m \), we need to express the number of boxes folded by each person as a function of \( m \).

1. **Jake's Boxes**:
- Jake can fold 8 boxes per minute.
- He has already folded 10 boxes.
- Therefore, the equation for Jake is:
\[ b = 8m + 10 \]

2. **Alyssa's Boxes**:
- Alyssa can fold 6 boxes per minute.
- She has already folded 20 boxes.
- Therefore, the equation for Alyssa is:
\[ b = 6m + 20 \]

Now, we can combine these two equations into a system of equations:

\[
\begin{align*}
b &= 8m + 10 \\
b &= 6m + 20 \\
\end{align*}
\]

Looking at the options provided, the correct representation of the equations is:

**B.**
\[
b = 8m + 10 \\
b = 6m + 20
\]