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.
Let's use the variables 𝑥 and 𝑦 to represent the number of slices of pizza and cans of soda sold, respectively.
1. The profit from selling each slice of pizza is $3. So the profit from selling 𝑥 slices of pizza is 3𝑥.
2. The profit from selling each can of soda is $2. So the profit from selling 𝑦 cans of soda is 2𝑦.
3. The total number of items sold is 200. So, 𝑥 + 𝑦 = 200.
4. The total profit made is $550. So, 3𝑥 + 2𝑦 = 550.
Therefore, the pair of linear equations that model this situation is:
𝑥 + 𝑦 = 200
3𝑥 + 2𝑦 = 550.