Which taxi company?

Which taxi company?

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about working out the cheapest option. 

two taxis

Two taxis from different firms are on a taxi stand. Heta asks the drivers their prices, and finds that Panther Taxis charge $3.00 at the start of the trip, and then $1.10 per kilometre. 
Gazelle Taxis charge $2.00 at the start, but then charge $1.20 per kilometre.

Question 1Change answer

a)  What would Panther Taxis charge for a 10 km journey? $ 

Question 1Change answer

b)  What would Gazelle Taxis charge for the same journey? $ 

Question 2Change answer

c)  Heta realises that he has to travel 15 km. Which would be the cheaper taxi?
     Explain your working or reasoning.

Question 3Change answer

d)  Complete the sentence below describing how to get the cheapest trips from the two companies:
"For journeys of up to  km, it would be cheaper to choose PantherGazelle Taxis, but for longer journeys it would be cheaper to choose PantherGazelle Taxis."
Task administration: 
This task is completed with pencil and paper or online.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
linear equations, money, breakeven points, simultaneous equations
Description of task: 
Students solve a number of mathematical problems involving money and distance, and compare the results to identify the cheapest taxi company.
Curriculum Links: 
Equations and expressions Level 4/5
This resource can help to identify students' ability to use inverse operations to solve simple linear relationships.
 

Key competencies
This resource involves showing how to solve two simple linear equations simultaneously. This relates to the Key Competency: Using language, symbols and text.

For more information see http://nzcurriculum.tki.org.nz/Key-competencies

Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 4-5
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y8 (06/1996)

Y9 (06/1996)
a) 14.00 [$3.00 + 10 × $1.10] easy very easy
b) 14.00 [$2.00 + 10 × $1.20] easy very easy
c) Panther Taxis would be cheaper ($19.50 as against $20). 
[Accept a logical deduction without a calculation, stating that the running costs of Panther Taxis are always less, once the breakeven point of 10 km is reached.		 easy easy
d) •   9 or 10 km;
•   Gazelle Taxis;
•   Panther Taxis.

[The equation would be 300 + 110k = 200 + 120k, leading to k = 10. If part kms are charged k could = 9.]

 very difficult difficult

NOTE: An algebraic calculation is not needed to answer parts c) and d) correctly.