Question

The Math Club sold slices of
pizza, p, at a profit of $3 each
and cans of soda, s, at $2 each
to raise money for a trip. They
sold 200 items and made a profit
of $550. Write the pair of linear
equations that model this
situation. (2 points)Equation to represent the total
number of items sold:=200
Equation to represent the total profit:=550

Answer 1

To model the situation with a pair of linear equations, we can define the following variables:

- Let \( p \) be the number of slices of pizza sold.
- Let \( s \) be the number of cans of soda sold.

From the problem statement, we can derive the following equations:

1. **Equation to represent the total number of items sold:**
\[
p + s = 200
\]

2. **Equation to represent the total profit:**
The profit from selling pizza is \( 3p \) (since each slice has a profit of $3), and the profit from selling soda is \( 2s \) (since each can has a profit of $2). Therefore, the total profit equation is:
\[
3p + 2s = 550
\]

Thus, the pair of linear equations that model this situation is:

1. \( p + s = 200 \)
2. \( 3p + 2s = 550 \)