First, calculate how much pizza is enough for one person. Then, compute how much pizza is needed for 8 people. Write the combinations that gives enough pizza along with their costs.
B
b
Write the different ways of buying three pizzas and pick the one that is cheaper and gives enough pizza for 8 people.
C
c
Compute the circumference of each pizza. Write some combinations that give enough pizzas along with the total circumference.
A
a
Two 14-inch pizzas. The area is 98Ï€ in^2 and the cost is $25.98.
B
b
Two 10-inch pizzas and one 14-inch pizza. Buying three 10-inch pizzas is the cheapest option, but it is not enough pizza.
C
c
Four 10-inch pizzas. The total circumference is 40Ï€ inches.
Practice makes perfect
a
First, we remember that the area of a circle is given by A=Ï€ r^2 and that the diameter is twice the radius. With this information, let's compute the radius of a 12-inch diameter pizza.
12 = 2r ⇒
r = 12/2 = 6
Next, we find the area of this pizza.
A = π(6)^2 ⇒ A = 36π in^2
According to the given information, this pizza is enough for three people. By dividing this area by 3, we will find how much pizza is enough for each person.
36Ï€/3 = 12Ï€ in^2
Now we want to buy pizzas for 8 people, so the amount of pizza needed is 8* 12Ï€ or 96Ï€ in^2. Let's find the area of the pizzas of different sizes.
Diameter (in)
Radius (in)
Area (in^2)
Cost ($)
10
5
P_1 = 25Ï€
6.99
14
7
P_2 = 49Ï€
12.99
Next, let's consider the different ways of buying the pizzas so that it is enough for the 8 people.
Pizzas Required
Amount of Pizza (in^2)
Cost ($)
4 small pizzas
100Ï€
27.96
2 small pizzas and 1 large
99Ï€
26.97
2 large pizzas
98Ï€
25.98
As we can see, in order to spend as little money as possible we must buy two 14-inch pizzas.
b
In Part A, we concluded that 8 people can eat with 96Ï€ in^2 of pizza. We also found the area of each pizza.
Size
Area (in^2)
Cost ($)
Small
P_1 = 25Ï€
6.99
Large
P_2 = 49Ï€
12.99
In this part we want to buy three pizzas. In the following table, we will write different ways to do it with the total costs.
Number of Pizzas
Area (in^2)
Cost ($)
Enough Pizza?
3 small
75Ï€
20.97
No
2 small and 1 large
99Ï€
26.97
Yes
1 small and 2 large
123Ï€
32.97
Yes
3 large
147Ï€
38.97
Yes
The first option is the cheapest one, but it will not be enough pizza for the 8 people. Therefore, we conclude that the second option is the cheaper one.
c
Since we want as much of the thick outer crust as possible, we will start by computing the circumference of each type of pizza. For this, we will use the formula C=2Ï€ r.
Size
Radius
Circumference
Small
5
C_1 = 2Ï€(5) = 10Ï€
Large
7
C_2 = 2Ï€(7) = 14Ï€
Let's write some options we have to buy enough pizzas for the 8 people along with the total circumference.
Number of Pizzas
Area (in^2)
Circumference (in)
4 small
100Ï€
40Ï€
2 small and 1 large
99Ï€
34Ï€
1 small and 2 large
123Ï€
38Ï€
2 large
98Ï€
28Ï€
From the options in the table above, we can see that the option that gives as much of the thick outer crust as possible is the first one.
