Question

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

Answer 1

Let's define two variables to represent the quantities involved:

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

Based on the situation described, we can set up 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 \( 3p \) (as each slice has a profit of $3), and the profit from selling soda is \( 2s \) (as each can has a profit of $2). Therefore, the equation for the total profit will be:
\[
3p + 2s = 550
\]

So, the pair of linear equations that model the situation is:
1. \( p + s = 200 \)
2. \( 3p + 2s = 550 \)