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### Part A:
We are given the function $ f(x) = 18x $, which represents the price Vincenzo's Pizzeria charges for $ x $ large specialty pizzas. The pizzeria runs a promotion on Tuesdays offering 20% off total orders.

So, the cost on Tuesday would be:
- 20% off means the price is reduced by $ 20\% $, or $ 0.20 $, so the customer pays $ 80\% $ of the regular price.
- This means we multiply $ f(x) = 18x $ by $ 0.8 $ (since $ 1 - 0.2 = 0.8 $).

Thus, the function for the price on Tuesday is:
\[
p(x) = 0.8 \times 18x = 14.4x
\]

Looking at the choices:
- Option A: $ p(x) = 0.8(18x) $ is correct.

### Part B:
Find the cost of ordering 3 large specialty pizzas on Saturday and on Tuesday.

1. **Saturday**:
   The cost of 3 pizzas at the regular price is:
   \[
   f(3) = 18 \times 3 = 54 \, \text{dollars}
   \]

2. **Tuesday**:
   The cost of 3 pizzas on Tuesday with the 20% discount is:
   \[
   p(3) = 0.8 \times 18 \times 3 = 0.8 \times 54 = 43.2 \, \text{dollars}
   \]

### Summary:
- **Saturday cost**: \$54
- **Tuesday cost**: \$43.20

Would you like further details or have any questions about the solution?

### Related Questions:
1. How would the function change if the discount on Tuesday was 30% instead of 20%?
2. If someone buys 5 large specialty pizzas on Tuesday, how much would they save compared to Saturday?
3. What if the price of each pizza increased by 10%, how would that affect the function?
4. How would you model the total cost for ordering $ x $ pizzas, assuming tax is added at 5%?
5. What is the percentage savings if someone buys 4 pizzas on a Tuesday versus a Saturday?

**Tip**: When calculating discounts, always multiply by the remaining percentage to get the discounted price!

The function f(x) = 18x represents the price Vincenzo's Pizzeria charges for x large specialty pizzas. The pizzeria is running a promotion for 20% off total orders on Tuesdays.
a. Which function p(x) represents the total cost of ordering large specialty pizzas on a Tuesday?

b. Find the cost of ordering 3 large specialty pizzas on a Saturday and on a Tuesday.

Learn how to calculate the cost of ordering pizzas with a 20% discount at Vincenzo's Pizzeria. This problem involves linear functions and basic algebra, suitable for students in Grades 6-8.

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