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4.3
Interpreting a Word Problem
P
urpose
The role this topic plays in quantitative reasoning
Throughout life you will encounter problems that require logic and quantitative reasoning. This section
will develop your ability to understand and conceptualize such problems with the use of symbols. For
example, you may need to know how to compute your payment for work done at a grocery or retail store
where your pay is dependent upon the hours you work, whether you worked overtime, and whether
you are paid a commission (a percentage of your sales). Your company may give this information as a
formula or you may have to compute the formula yourself.
A word problem describes the context of the problem. It also provides information about the important
variables in the situation. Finally, it provides insight into the potential relationship between the variables
in the problem. This experience will help you to see the context more clearly, identify which of the
variables are critical, and help you establish the relationship among the variables to help solve the
problem you define.
L
earning Goals
What you should learn while completing this activity
1. To precisely define the problem represented in the word problem
2. Identify variables, constants, relationship, and assumptions when working with quantitative problems
3. Translate English statements (that are sometimes ambiguous) into precise and accurate mathematical
statements
4. Validate that a word problem solution is mathematically correct and makes sense back in the real
world situation.
D
iscovery
Finding out for yourself
Create your own word problem. Look around your life, think about what has happened in the last few
days, and create a word problem to bring to class.
One example might be determining where to have lunch:
“My family just got into town and haven’t eaten since last night. We all want to have a healthy meal
that’s relatively inexpensive. At the same time, the family includes a vegetarian, a carnivore (he
loves meat!), someone on a Paleo diet, and Aunt Georgia who really wants a salad. Where do we
go? There’s a local farmer’s market-type store an extensive salad and food bar and the cost is $8.95
per lb. The choices range from very light-weight exotic salads (expensive in stores) to very heavy
noodles (cheap in stores). What is the best strategy for stopping at a lunch place given the constraints
and also in choosing the food for lunch?”
Here’s another example:
“Last night I was with a group of friends and we went downtown to play poker. There were a set of
chips, and we needed to determine how many chips each player should get. The number of players
were going to be either 6 or 7 and we had 1,000 chips. The maximum number of chips, per person