Cost of a Pizza A pizza parlor charges 12 for a cheese...

Cost of a Pizza A pizza parlor charges $\$ 12$ for a cheese
pizza and $\$ 1$ for each topping.
(a) How much does a 3-topping pizza cost?
(b) Find a formula that models the cost $C$ of a pizza with
(c) If a pizza costs $\$ 16,$ how many toppings does it have?

$$n=1 \quad n=4$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solving Linear Equations

This involves isolating the variable in a linear equation to determine its value given certain conditions. In the context of the problem, when the total cost is provided, solving the equation allows for determining the number of toppings on the pizza.

Linear Relationships

A linear relationship is one in which there is a constant rate of change between two variables. The problem illustrates this through the direct, additive relationship between the number of toppings and the overall cost, allowing for the formulation of a simple linear equation.

Algebraic Modeling

This concept involves representing real-world relationships using algebraic expressions or functions. In the problem, the total cost is modeled as a linear function of the number of toppings by combining a constant base cost with a variable cost that depends on the topping count.

Fixed and Variable Costs

Fixed costs refer to expenses that do not change with the level of production or, in this case, the number of toppings, such as the base price of the pizza. Variable costs change in direct proportion to the number of units produced or services added, such as the cost per topping. Together, these concepts allow for clear cost analysis and modeling.

Transcript

Please give Ace some feedback