Washing machine repair

Washing machine repair

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about calculating and comparing the cost of repairs from two companies.

Two washing machine repair firms charge for repairs in different ways.

  • Nockem Hardware charge a standard $70 for a call out, and then $30 per hour for servicing.
  • Bustum Services charge $40 for the call out, and then $35 per hour for servicing.
a)

 

 Show how to work out what Nockem Hardware would charge for a 2 hour repair.

  

Answer: $__________
 
b)

 
Show how to work out what Bustum Services would charge for a 2 hour repair.

 

 Answer: $__________
 
c)

 
Show how to work out how many hours it would take to carry out a repair for which both companies charged exactly the same.

  

Answer: __________ hours
 
d)

 
 
Mrs Savi knows that her machine is badly damaged and will take 3 hours to fix.
  • Recommend which firm it would be cheaper for Mrs Savi to get her machine repaired by.
  • Give reasons for your recommendation (justification).  
Recommendation:
 
 
Write the reasons for your recommendation (justify with any working you did).  
 
 
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Key Competencies: 
Using language, symbols, and texts
Keywords: 
linear equations, money, breakeven points, simultaneous equations
Description of task: 
Students calculate the repair charges for two different washing machine repair companies, and compare and explain their results.
Curriculum Links: 
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.
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 (11/2004)
a)
 		 $130
$70 + 2 × $30 or other working that uses the information given to show the amount it would cost for a 2 hour repair.		 very easy
very easy
b) $110
$40 + 2 × $35 or other working that uses the information given to show the amount it would cost for a 2 hour repair.		 easy
very easy
c) 6
For any 1 of:

  • Nockem: $70 + 6 × $30 = $250 and
    Bustum: $40 + 6 × $35 = $250;
  • other working that uses the information given to show the amount it would cost for a 6 hour repair and how they arrived at 6 hours, e.g., 70h + 30 = 40h + 35, 30h = 5; or
  • 70 - 40 = 30, $35 - $30 = $5, 30 ÷ $5 = 6.
 difficult
moderate
d) Bustum Hardware, and any 1 of:

  • comparison of Nockem and Bustum's charges for 3 hours, i.e.,
    Nockem: $70 + 3 × $30 = $160
    Bustum: $40 + 3 × $35 = $145;
  • for any work under 6 hours, Bustum will be cheaper due to its lower call out/house visit rate;
    [or answer consistent with answer given in c)]
  • other acceptable explanations.
 moderate

Results are based on a trial set of 200 students. 

NOTE: In parts a), b), and c) students can gain a mark for showing their strategy if they use a correct method, but make some computational errors, leading to an incorrect final answer.

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
a)
b)
d)		 200
150
300 and 225		 100 × 2
75 × 2
100 × 3 and 75 × 3		 Adds the call-out cost to the hourly rate before multiplying by the number of hours.
a)
b)		 60
70		 30 × 2
35 × 2		 Calculates the hourly rate only, without adding on the call-out costs.
Other ARB resources
For similar resources involving linear equations and comparing costs at level 4 refer to: Rescue helicopters and Which taxi?