Page 162 - qrps

Quantitative Reasoning & Problem Solving
162 © 2014 Pacific Crest
Scenario:Picking Pizzas! Elissa and her nephew, Chuck, are going out for pizza to celebrate his
excellent performance in college last semester. This time around, Chuck is treating.
Chuck knows that one small pizza will not be enough for the two of them. The menu
at their favorite place, Angelo’s, 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
pizzas each have eight slices. Chuck has $25 on him, and he doesn’t mind taking
home the leftovers for tomorrow’s breakfast. The small pizza is 8 inches in diameter,
the medium is 12 inches in diameter, and the large has a 16 inch diameter. Using
these facts, which choice gives the most pizza for the money? Chuck is a finance
major and really enjoys this kind of problem solving. Elissa isn’t so sure but watches
closely as Chuck uses the methodology.
Step Watch it Work!
1. Define the
problem
Chuck and Elissa want to find the best pizza purchase for the money.
2. Identify key
issues
Enough pizza must be bought for at least one meal.
One small pizza will not be enough.
Chuck does not mind having leftovers.
3. Collect
data and
information
Chuck has $25.
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
doesn’t provide any helpful information, since pizzas of different sizes can be cut
into the same number of slices. The small pizza could even be cut into 12 slices.
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 apart
One aspect to look at is the comparative sizes of the pizzas. This is one 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.