Bike repairs

Bike repairs

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about graphing and solving linear equations.
Adam needs to find someone to mend his mountain bike.
The local bike shop says that this will cost $15 plus $2 per minute of time they spend fixing it.
 
This can be written as the equation:

c = 2t + 15

where c is the cost in dollars
t is the time spent in minutes
 

a)

Fill in the costs in this table for each of the times given.

table to complete

mountain bike
b)
 
This rule can be drawn as a graph. Plot the points from the table in a) on this graph.
 
                Cost of Fixing a Mountain Bike per Minute Spent in Repair
graph
 
c)
 
If the repairs took 35 minutes, what was the cost? $__________ 
 
d)
If the job cost $45, how long did the repairs take? __________ minutes
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
linear equations, graph construction, substitution
Description of task: 
Students complete a table and a graph of an equation about the costs of bike repairs, then interpret the graph to respond to questions.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
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: 

  

Y10 (10/1999)

a)

35, 55, 75, 95

easy

b)

answer on graph
NOTE: Accept if a bar graph, or graph of step function is used, or points are joined (the appropriate use of line graphs for this type of situation could be further discussed).  
Also accept if answers from a) are correctly plotted.

all correct – moderate

1-2 errors – easy

c)

 85 [Accept if consistent with a) or b)]

easy
d) 15 [Accept if consistent with a) or b)] easy
Diagnostic and formative information: 
   Common error Likely reason
a)

20, 40, 60, 80
25, 35, 45, 55

Ignores +15 in equation.
Increases as t rather than 2t.
b) Bends line to go through origin rather than through (0, 15)