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

Equation to represent the total number of items sold: _________ = 200

answers for this one:

p + 3

3s

p + 5


Equation to represent that total profit: ______ = 500

answers for this one:

3p + 2s

2p + 3s

p + s

Answer 1

you sure

Answer 2

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

Answer 3

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!