### Student Page 3.1.2 Pricing Pizzas

Pizza restaurants let you customize your pizza. You can also order specialty pizzas. Are you getting a good deal? If so, how good is the deal are you getting? If not, why is the deal not so good?

Work together to analyze the pricing of a pizza restaurant. Use a pizza restaurant's website for a location close to you as sometimes different locations of the same chain charge different prices. Each group should choose a different pizza size or crust type to investigate. Fill in the table as you go and share your work with the class.

#### 1.

Play with a pizza restaurant's online menu to determine prices requested in the table below. Check prices on more than one ingredient to determine if the prices are the same or different based on ingredient type. For example, are meats more expensive than veggies? Fill-in Table 3.1.2.1.

Description | Small, original crust |
Medium, original crust |
Large, original crust |
Large, thin crust |
Extra Large, original crust |
---|---|---|---|---|---|

Diameter of pizza | 10 inches | 12 inches | 14 inches | 14 inches | 16 inches |

Price of Plain Cheese Pizza |
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Cost of one topping on pizza |
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Price of Cheese Pizza with 1 topping |
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Price of Cheese Pizza with 2 toppings |
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Price of Cheese Pizza with 3 toppings |
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Price of Cheese Pizza with 4 toppings |
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Price of Cheese Pizza with 5 toppings |
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Price, \(P\text{,}\) of Cheese Pizza with \(t\) toppings (equation) |

#### 2.

For each type of pizza, find an equation that gives the price of a pizza with \(t\) toppings. Write the equation in the last row of the table above.

#### 3.

Compare the equations for each pizza type. If you graph these equations, which graph would you expect to be steepest? Why?

#### 4.

Using an electronic graphing tool and different colors for each pizza size/crust type, graph all of the pizza data. Choose appropriate scales for each axis. Label the scales and titles. Label each graph with pizza size and crust type. Compare the graphs. What do you notice?

#### 5.

##### (a)

Which graph is the steepest? What is the slope of the steepest graph?

##### (b)

How does the slope show up in the table?

##### (c)

How does the slope show up in the equation?

#### 6.

##### (a)

Which graph has the largest \(y\)-intercept?

##### (b)

How can you tell from the graph?

##### (c)

How can you tell from the table?

##### (d)

How can you tell from the equation?

#### 7.

Choose two different specialty pizzas from the same pizza restaurant as previous problems. For each specialty pizza:

##### (a)

Use the pizza restaurant's website to find the price for each pizza size. Fill in Table 3.1.2.2.

##### (b)

Determine the price if you customized the pizza instead of ordering the specialty pizza.

##### (c)

Which is the better deal? Why?

#### 8.

Choose one size of pizza. Show your work as you answer each problem. Write your answers in Table 3.1.2.2.

##### (a)

Determine the price of a pizza with 8 toppings.

##### (b)

Determine the number of toppings you can get for $25.

Description | Small, original crust |
Medium, original crust |
Large, original crust |
Large, thin crust |
Extra Large, original crust |
---|---|---|---|---|---|

Price of speciality pizza (list name): |
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Number of toppings on pizza |
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Customized price | |||||

Which is the better deal? Why? |
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Price of speciality pizza (list name): |
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Number of toppings on pizza |
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Customized price | |||||

Which is the better deal? Why? |
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Price of a pizza with 8 toppings |
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Number of toppings you can get for $25 |

Share how you determined your responses in Table 3.1.2.2, and particularly for the solutions to Student Page Exercise 3.1.2.7. Keep track of approaches different students used to solve Student Page Exercise 3.1.2.7 and Student Page Exercise 3.1.2.8. What similarities were there in solution strategies?

What strategy do you want to remember when determining the price of a pizza with 8 toppings? What strategy do you want to remember when determining how many toppings you can afford for $25? Apply those strategies to solve the following problems:

#### 9.

You're going to the state fair. The entrance fee is $15. Each ride costs $3.

##### (a)

Determine an equation that gives the total amount you will pay for entrance and rides based on the number of rides.

##### (b)

Use the equation to determine the amount you will pay for admission and rides if you ride 6 rides.

##### (c)

You have $45 to spend for the fair. How many rides can you take?

#### 10.

Your favorite clothing store has a storewide 20% off sale going on.

##### (a)

Determine an equation that works for the sale for every original price of items.

##### (b)

What is the sale price for a $35 shirt?

##### (c)

What was the original price of an item you paid $47 to buy?

How does the context help you decide how to solve each problem? How does the context help you determine for which variable you're solving?