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

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