The topic of spending offers all kinds of interesting mathematical applications in algebra, pre-algebra and beyond. Students can compare different coupons or discounts, various payment plans or things like cell phone plan options, and many interesting discussions can be had around the idea of wants vs. needs.

Highlighted Problem: From Here to There:

Recently I traveled to the city of Graphton, and after I landed at the airport I needed to get downtown to my hotel. I investigated my ground transportation options, and found the following:

  • A bus runs from the airport and stops at all downtown hotels for a $15.00 fee.
  • Taxis in Graphton charge an initial fee of $2.00 for the first 1/4 mile or fraction thereof plus $0.25 for each additional 1/4 mile or fraction thereof.
  • A motorcycle shuttle (with sidecar for luggage) charges an initial fee of $3.00 plus an additional 1 cent per second.

For each transportation option, pick the graph below that you think best illustrates the cost of riding it to my hotel. For each graph you choose, explain why you think it’s the best fit and include the units that you would put on each axis.

This problem can begin some terrific discussion around modeling and graphical representations of real world situations.

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