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.

Question

(1 point)
Equation to represent the total number of items sold:
Equation to represent the total profit:
= 550
= 200

Answer 1

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

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

We have two key pieces of information to form our equations:

1. The total number of items sold is 200: \[ p + s = 200 \]

2. The total profit from selling pizza and soda is $550. The profit from pizza is $3 per slice, and the profit from soda is $2 per can: \[ 3p + 2s = 550 \]

Putting these together, we have the pair of linear equations that represent the situation:

1. Total number of items sold: \[ p + s = 200 \]

2. Total profit: \[ 3p + 2s = 550 \]

These two equations can be used to solve for the values of \( p \) and \( s \).