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Comparative Analysis of Taxi Fare Structures from Three Companies

This analysis compares the charging structures of three taxi companies: Fred's Taxi Company, P&G Taxi Company, and FlatRate Taxi Company, using equations and graphical representations to visualize costs. Each company's fare is determined by either fixed rates or distance-based pricing. Calculations reveal that P&G is the most cost-effective choice for short distances (up to 24 km), while FlatRate offers better value beyond that. Recommendations are provided based on specific destinations within the city.

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Comparative Analysis of Taxi Fare Structures from Three Companies

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  1. 1.4 Practice 1

  2. Represent the three taxi companies' charges using the same representation, for example, three equations or three graphs with the same variables and scale.

  3. three equations • Fred’s Taxi Company • Come with us! • Fixed charge: $5.00 • Per kilometre: $0.50

  4. Given • P and G Taxi Company • Cheap rates! • C = 0.65D + 2

  5. Flatrate Taxi Company • Our advantage is clear! • $25.00 flat fee to any destination up to 60 km.

  6. three graphs

  7. City • Recommend which taxi company to use for a trip to two of the common destinations. • Fred’s cost to city = 0.5 x 17 + 5 = $13.50 • P&G: C = 0.65x 17 + 2 = $13.05 • Flatrate = $25 • P&G is cheapest

  8. Port • Fred’s cost to city = 0.5 x24 + 5 = $17.00 • P&G: C = 0.65x 24 + 2 = $17.60 • Flatrate = $25 • Fred’s is cheapest

  9. Bethlehem • Fred’s cost to city = 0.5 x45 + 5 = $27.50 • P&G: C = 0.65x 45 + 2 = $31.25 • Flatrate = $25 • Flatrate is cheapest

  10. Read 17, 24 and 45 off the graph

  11. Recommend distances for which it would be cheapest to use P and G Taxi Company.

  12. From 0 up to 20 km

  13. You can do a simultaneous equation to confirm this value • C = 0.5D + 5 • C = 0.65D + 2 • 0=0.15D-3 • D=3/0.15 = 20

  14. Marking schedule- ACHIEVED • Student must select and use at least threedifferent methods, for example, formulae, graphing, or simultaneous equations:

  15. Fred, who owns Fred’s Taxi Company, wants to be the cheapest taxi company people can use to travel to any destination. • Write and describe at least two different ways Fred could realistically change his charges to achieve this goal. Include specific examples of the rates he could use.

  16. For example, a student might demonstrate understanding of concepts and communicate their chain of reasoning by solving Fred and PG equations simultaneously and using the solution to determine appropriate selections for different distance ranges

  17. Fred = 0.5 x 24 + 5 = $17 • PG = 0.65 x 24 + 2 = $17.60 • Flat = $25 • Use Fred because it is the cheapest.

  18. Use the graph to establish who is cheapest in each section

  19. Now make sure he has the cheapest rate in each section.

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