A pizzeria charges $6.99 for a cheese pizza plus $1.25 for each additional topping. Their costs are approximately $2.50 for each cheese pizza and $0.60 per topping. Which function models how much the pizzeria earns on a pizza with x toppings?
A.	P(x) = (6.99 + 1.25x) + (2.50 + 0.60x)
B.	P(x) = (6.99 − 1.25x) + (2.50 + 0.60x)
C.	P(x) = (6.99 + 1.25x) − (2.50 − 0.60x)
D.	P(x) = (6.99 + 1.25x) − (2.50 + 0.60x)

To determine how much the pizzeria earns on a pizza with $ x $ toppings, we need to calculate the profit. Profit is the difference between the revenue and the costs.

1. **Revenue calculation**:
   The revenue from selling a pizza with $ x $ toppings is given by:
   \[
   R(x) = 6.99 + 1.25x
   \]
   Here, $ 6.99 $ is the price for a cheese pizza, and $ 1.25 $ is the additional charge for each topping.

2. **Cost calculation**:
   The cost to make a pizza with $ x $ toppings is given by:
   \[
   C(x) = 2.50 + 0.60x
   \]
   Here, $ 2.50 $ is the cost for a cheese pizza, and $ 0.60 $ is the cost for each additional topping.

3. **Profit calculation**:
   The profit function $ P(x) $ is the revenue minus the costs:
   \[
   P(x) = R(x) - C(x)
   \]

Substituting the expressions for $ R(x) $ and $ C(x) $:
\[
P(x) = (6.99 + 1.25x) - (2.50 + 0.60x)
\]

Thus, the correct function that models how much the pizzeria earns on a pizza with $ x $ toppings is:
\[
\boxed{D. P(x) = (6.99 + 1.25x) - (2.50 + 0.60x)}
\]

Would you like further details or have any questions?

Here are 8 related questions that expand on this information:
1. How would the profit function change if the cost per topping increased to $0.75?
2. What is the profit for a pizza with 3 toppings?
3. How many toppings would make the profit zero?
4. What is the break-even point for the number of toppings?
5. How does the profit change if the price of the cheese pizza is increased to $7.50?
6. What if the pizzeria decides to offer a discount of $0.50 per topping, how does the function change?
7. If a customer buys a pizza with 5 toppings, what would be the total revenue and cost?
8. How would a fixed delivery charge of $3 affect the profit function?

**Tip**: Understanding how to form and manipulate profit functions is key to optimizing business strategies and pricing models.

Explore how to model profit on pizzas with toppings using mathematical formulas. Understand the revenue and cost calculations involved in determining profit for a pizzeria. Suitable for high school students.

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