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

Answer 1

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

• 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 two key pieces of information:

1. The total number of items sold (pizza slices and soda cans) is 200: \[ p + s = 200 \]

2. The total profit from the sales of pizza and soda is $550. Since each slice of pizza sold at a profit of $3 and each can of soda sold at a profit of $2, we can express the profit equation as follows: \[ 3p + 2s = 550 \]

Therefore, the pair of linear equations that model the situation is: \[ \begin{align*}

1. & \quad p + s = 200 \
2. & \quad 3p + 2s = 550 \end{align*} \]