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
?

Answer 1

To represent the number of boxes folded by Jake and Alyssa based on the minutes worked, we can create equations for each person.

For Jake:
- He can fold 8 boxes per minute and has already folded 10 boxes.
- The equation for the number of boxes he will fold after \( m \) minutes is:
\[
b_J = 8m + 10
\]

For Alyssa:
- She can fold 6 boxes per minute and has already folded 20 boxes.
- The equation for the number of boxes she will fold after \( m \) minutes is:
\[
b_A = 6m + 20
\]

We can represent the total number of boxes folded by both Jake and Alyssa combined as:
\[
b = b_J + b_A
\]
Substituting the equations for \( b_J \) and \( b_A \):
\[
b = (8m + 10) + (6m + 20)
\]
This simplifies to:
\[
b = (8m + 6m) + (10 + 20) = 14m + 30
\]

Thus, the system of equations representing the number of boxes folded by Jake and Alyssa based on the minutes worked is:

1. \( b_J = 8m + 10 \)
2. \( b_A = 6m + 20 \)

Or, if considering the total folded boxes:
- \( b = 14m + 30 \)