You decide to open a pizza parlor. The ingredients require...

You decide to open a pizza parlor. The ingredients require that you charge $\$ 4.50$ for a 7.0 -in. -diameter pizza. How large should you make a pizza whose price is $\$ 10.00$ , assuming the cost is based entirely on the cost of ingredients? (a) 1.4 in. (b) 3.1 in. (c) 7.0 in. (d) 10 in. (e) 16 in.

You decide to open a pizza parlor. The ingredients require that you charge $\$ 4.50$ for a 7.0 -in. -diameter pizza. How large should you make a pizza whose price is $\$ 10.00$ , assuming the
cost is based entirely on the cost of ingredients?
(a) 1.4 in. (b) 3.1 in. (c) 7.0 in.
(d) 10 in. (e) 16 in.

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Key Concepts

Scaling and Proportions

This concept involves setting up and solving equations that arise from the proportional relationship between two quantities. By determining the scaling factor from a known case, one can extend the relationship to a new scenario. This is particularly useful in geometry and real-world pricing problems where dimensional changes affect the final outcome.

Direct Proportionality

In many real-world applications, one quantity may be directly proportional to another. In this context, if the cost is determined solely by the ingredients required, then the cost is directly proportional to the area. This means that if the area doubles, the cost also doubles, and it provides the basis for setting up a proportion to solve for unknown quantities.

Area of a Circle

This concept involves understanding that the area of a circle is given by the formula A = ?r² (or equivalently A = (?/4)d² when using the diameter). Knowing the area is critical when calculations depend on the size of a circular object, especially in problems where cost or resources are based on area.

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