Mathematical Problem Solving

Here are three scenarios involving a hypothetical friend of yours facing some sort of problem or decision that they are facing. Choose one of these scenarios — the one that sounds the most interesting to think through — and create a problem solving pathway to address the situation. That is, (1) identify the question that needs to be answered, (2) work backwards, identifying “smaller” questions that the big question relies on, (3) continue doing this until you’ve reached questions that you can resolve though doing research, doing a calculation, or making a reasonable assumption, (4) answer those questions, and (5) piece everything together to answer the original question.

Scenario One: Moving for a Better Job

Suppose your friend is working as a bank teller full-time here in Grand Junction at the Wells Fargo downtown. While she likes her job, she does wish she made more money. There have been rumors lately that there are openings for bank manager and personal banker positions at some Wells Fargo branches in Denver, Boulder, Colorado Springs, and other cities on the front range. Your friend is considering looking up and applying to these jobs, but is concerned whether or not it’s even worth it.

Sure she’d make more money at one of these jobs on the front range, but how much more? Enough to cover the higher cost of living expenses in the city? Wouldn’t the higher income at one of these jobs mean she’d have to pay more in taxes? How much more? Maybe it’d be easier to ask for a raise as a teller here in Grand Junction; after all she’s being paid the same hourly wage she was when she started two years ago. What’s the starting wage of a teller here today? Maybe even if the money isn’t substantially better, there are other benefits of the jobs on the front range that’s she not getting as a teller now that would make it worth the move. Maybe there are other financial factors she hasn’t even considered yet!

Should your friend try to get a job as a bank manager or personal banker on the front range or keep working in Grand Junction as a teller?

Scenario Two: Selling a Car to Buy a Motorcycle

Your friend is considering selling his 2008 Toyota Corolla and buying a motorcycle. He wants a new motorcycle, and has been looking at a Honda NC750X. He plans to ride it to-and-from work eight miles from his house every day, and over to the front range to go to a concert with his buddies about once a month. He’s excited by the idea of saving money on gas, but concerned about how much he’ll have to pay for the bike (and how long he’ll be making payments) after he sells his Corolla to make down payment. He is unsure about maintenance costs though; Toyotas are famously reliable, and maybe he’ll have to pay more each year to keep a motorcycle in good shape.

Your friend is also wary about safety. Although he doesn’t know the exact details he does have a foggy idea that riding a motorcycle is more dangerous than driving a car.

Should your friend sell his car for the motorcycle?

Scenario Three: Saving Money on Coffee

Coffee is expensive! Your friend is a student here at CMU. This semester she’s got an 8am Monday/Wednesday/Friday class, and every morning she’s been buying a tall coffee from the campus Starbucks to cope. She knows this will cost way too much money if she keeps doing it for the rest of the semester, and is looking for a better routine to get her coffee fix!

Your friend could buy her coffee elsewhere each morning. Rowdy’s, the convenience store in the University Center, sells coffee, and so does the Circle K across North Ave. Your friend has even heard that these spots offer discounts or punch-cards if you buy enough coffee, or if you bring your own thermos for coffee. Alternatively she could just start making her own coffee and bringing it to campus each morning. But she’s never done this before, and she’d need to buy a coffee machine (nothing fancy), and filters, and the ground coffee itself. She doesn’t even know how much ground coffee is recommended to use when brewing a cup!

Help your friend decide how to save the most money buying or making coffee for class this semester.