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. The sold 200 items and made a profit of $550. Write the pair of linear equations that model this situation.

To model the situation with the Math Club selling pizza slices and soda, we can establish two equations based on the information given:

1. Total number of items sold:
   Let \( p \) represent the number of pizza slices sold and \( s \) the number of cans of soda sold. According to the problem, the total number of items sold is 200. Therefore, the equation is: \[ p + s = 200 \]

2. Total profit made:
   The profit from each pizza slice sold is $3, so the total profit from pizza slices is \( 3p \). The profit from each can of soda sold is $2, so the total profit from soda is \( 2s \). The total profit earned was $550, leading to the equation: \[ 3p + 2s = 550 \]

Thus, the pair of linear equations that model this situation is:

1. \( p + s = 200 \)
2. \( 3p + 2s = 550 \)

Now, matching this with the provided answers:

1. For the equation representing the total number of items sold:
   Answer: \( p + s = 200 \) (none of the provided options match this exactly).

2. For the equation representing the total profit:
   Answer: \( 3p + 2s = 550 \) (so the correct choice here is the first option: \( 3p + 2s = 550 \)).

So to make it clear:

• The total number of items sold is represented by \( p + s = 200 \).
• The total profit is represented by \( 3p + 2s = 550 \).

Let's go through the problem step by step again to ensure clarity:

1. Understanding the Variables:

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

2. Total Items Sold:

   • The Math Club sold a total of 200 items (pizza slices + soda).
   • The equation representing this is: \[ p + s = 200 \]

3. Total Profit:

   • The profit from each pizza slice sold is $3, so the total profit from pizza slices is \( 3p \).
   • The profit from each can of soda sold is $2, so the total profit from soda is \( 2s \).
   • The total profit is stated to be $550.
   • The equation representing this is: \[ 3p + 2s = 550 \]

Thus, the system of equations is:

1. Equation for total items sold:

   • \( p + s = 200 \)

2. Equation for total profit:

   • \( 3p + 2s = 550 \)

Matching to Your Provided Answers:

• For the equation to represent the total number of items sold, the closest match would be \( p + s = 200 \), which is none of the options you provided.

• For the equation to represent the total profit, the correct formulation is \( 3p + 2s = 550 \), which matches the first option you provided.

Conclusion:

So to confirm:

• The total number of items sold is \( p + s = 200 \) (no provided option matches that).
• The total profit equation is indeed \( 3p + 2s = 550 \) (corresponds to the first option).

If there was any misunderstanding with the options or if they should align differently, please let me know for further clarification!