MSA Problem 2.3 Comparing Equations
Comparing Costs
Aim: Students will be able to make connections between linear equations and
Patterns in the tables and graphs; identify rate of change and y-intercept.
Procedure: Use the equations from 2.2 to launch the discussion (Teachers’ Guide p. 53).
DHenri = 45 + t
DEmile = 2.5t
Ask the students what the differences between the two equations are.
What information do the variables and numbers represent in each equation?
Present the story of Ms. Chang’s class, p. 28 – student book (typed up on worksheet)
Write on chart paper/chalkboard the two equations for the bids on the t-shirts
Cmighty = 49 + n
CNo Shrink = 4.5n
Have the students tell you what the numbers and variables mean in these equations,
Then ask them to complete the worksheet.
For those who finish quickly, ask them - “From which company will $120 buy the most T-shirts? How might they try to figure this out?
How would the answer to B, help in deciding which company to use to order T-shirts?
Other questions to use in connection with this problem:
ACE, p. 33 #4 a, b, c, (practice in making sense of graphs, reading information)
p. 34 #5, could be used as a quiz question; incorporate making a graph.
p. 35 #6 - instruct on how to plug coordinates into an equation to see if the numbers are in fact solutions to the equation (and therefore be a point on the line of that equation)
(this question relates to #5 on p. 34)
p. 36 # 9
p.37 #10
Name:______Date:______
MSA Problem 2.3
Ms. Chang’s class decides to give T-shirts to each person who participates in the Walkathon. They receive bids for the cost of the T-shirts from two different companies.
Equation
Mighty Tee charges $49 plus $1 per T-shirt. C = $49 + $1n
No-Shrink Tee charges $4,50 per T-shirt C = $4.50 n
(C = the cost and n = the number of t-shirts)
- For each company, what is the cost of 20 T-shirts?.
(use the equations above)
Mighty Tee ______
No-Shrink ______
- For what number of T-shirts is the cost the same no matter which
company is used? Complete the table below to find out.
Number ofTee shirts (n) / Mighty Tee Cost
$49 + $1 n / No Shrink Cost
$4.50 n
2 / $49 + $1 x 2 =
$49 + $2 = $51 / $4.50 x 2 = $9
4
6
8
10
12
14
16
18
20
Name: ______Date:______
MSA Investigation 2
Checking to see which pair of values would fit the equation.
!) The equation C = 10 + 2n represents the cost in dollars ‘C’, for ‘n’
painters caps advertising a walkathon. Which pair of values could
represent a number of caps and the cost for that number of
caps.
Substitute the values for n and C into the equation to see if they work.
Show your work. Then write yes or no next to the pair of values.
(n, C)C = 10 + 2n
(0, 10)
(7, 24)
(15, 30)
2)The equation d = 3.5t +50 represents the distance in meters, ‘d’, that a cyclist is from his home after ‘t’ seconds. Which pair of values would fit the equation?
(t, d)d = 3.5t + 50
(10, 85)
(0, 0)
(3, 60.5)