Page 139 - Foundations of Learning, 4th Edition (Revised)
P. 139
3 Collect data and Chuck has $25.
information
The menu lists three sizes: the small for $5, the medium for $8, and the
large for $11.
The small pizza has six slices and the medium and large pizza each
have eight slices.
The small pizza is 8 inches in diameter, the medium is 12 inches in
diameter and the large has a 16 inch diameter.
In examining this information, Chuck decided that the number of
slices really does not provide any helpful information. He is interested
in the quantity of pizza, not the number of slices.
4 Identify assumptions All pizzas ordered will be cheese only—no toppings.
The goal is to get the most pizza for the least amount of money.
5 Break the problem One aspect to look at is the comparative sizes of the pizzas. This is one
apart sub-problem.
Then, using cost, Chuck can calculate the amount of pizza per dollar.
6 Model sub-problems Comparison of pizzas:
Small pizza: 8 inch diameter (4 inch radius): Area = πr2= 16π
Medium pizza: 12 inch diameter (6 inch radius): Area = 36π
Large pizza: 16 inch diameter (8 inch radius): Area = 64π
Pizza per dollar:
For the small pizza, Chuck gets 16π ÷ 5 = 3.2π units per dollar.
For the medium pizza, Chuck gets 36π ÷ 8 = 4.5π units per dollar.
For the large pizza, Chuck gets 64π ÷ 11 = 5.8π units per dollar.
7 Integrate solutions Given the models, it looks like one large pizza is the best deal. But let’s
look at some other options.
If Chuck buys two small pizzas at $10, they only get 32π of pizza, vs.
64π for $1 more. Not a good deal.
If he buys a small and a medium pizza at $13, they get
(16 +36)π = 50π; less than one large pizza and for more money.
It looks like buying a large pizza makes the most sense and Chuck has
enough money as well.
8 Test and validate Is this convincing? It does appear that a large pizza is the way to go.
9 Generalize the The method of finding a common comparison, in this case, units of
solution pizza (via area) per dollar, can be generalized. Often, when buying
items, one needs to make this kind of comparison. Sometimes, you
may be surprised. Is 5 cans for a $1 better than 19¢ per can? Is an all-
day ticket at an amusement park for $40 better than $2 per ride?
10 Communicate the Chuck and Evelyn should order a large pizza for $11 and Chuck will
solution have the leftovers for a tasty breakfast.
Chapter 5 — Problem Solving Skills 133
