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Q
uantitative
R
easoning &
P
roblem
S
olving
190
© 2014 Pacific Crest
A
Successful Performance
Successful application of your learning looks like this
As you begin to apply what you’ve learned, you should have a good idea of what success looks like.
A SUCCESSFUL
PERFORMANCE
I solve word problems. I…
●
Provide a precise de
finition of the word problem
●
Identify the key issues, associated variables and critical assumptions
●
Translate the world problem into a set of mathematical relationships (model)
●
Validate the solutio
n produced from the mathematical model
D
emonstrate Your Understanding
Apply it and show you know in context!
Interpret and solve each of the following word problems.
1. Your bank assesses a $5.00 monthly fee for having a checking account and $0.20 for each check
you cash. At the end of the year, you reorder your checks for $10.00 for 100 checks, which is the
annual usage of checks. What is your monthly checking account cost?
2. In planning to go to the movies, you and two friends have collected cereal boxes that offer a movie
promotion. Six boxes can be converted to a free movie pass, while three boxes get you a food
voucher for $3.00. You and your friends have a total of 15 boxes saved, and you want to go to the
showing that costs $5.50. How should you optimize the use of the tickets, if you have three people
going to the theater? How much money do you need in order to make sure that everyone has $3.00
for food? The movie starts at 3:30 and is likely to sell out since it has gotten rave reviews.
3. In planning the party for Grandpa’s 80
th
birthday you are going to rent out the luxury suite at the
local country club. A promotion says that you must have a minimum of 40 people and that each
person will be charged $35. This includes full buffet for every person, the dedicated room, at-the-
table preparation of cherries flambé for dessert (1 dessert for every 5 people), valet parking for
every guest (value of $8) and free admission (general admission is $8). You plan on negotiating
the rate down to $25/person since the country club is undergoing some renovation and tends to
be far less busy during the Saturday of Thanksgiving week. You want to make it affordable for all
the grandchildren, so you will only charge them $5 per person. Given that 32 grandchildren and
friends plan to come to the party, what would be the cost for each of Grandpa’s children, given
that there are six siblings and each will be bringing their spouse?
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Model, the Methodology, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the hardest problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems. Try to determine which of the steps are the hardest
and what types of situations make these steps the hardest.
Can you still solve the problem? If so, solve it. If not, explain why not.
What are the conditions and parameters that make a word problem difficult to solve?