U.S. Shirts
U.S. Shirts Using Tables, Graphs, and Equations, Part 1
Learning Goals In this lesson, you will:
Use different models to represent a problem situation. Determine an initial value when given a final result. Identify the advantages and disadvantages of using a particular representation.
H
ave you ever wondered where your clothes come from? Who actually makes
the clothes you wear? For the most part, clothes are made in countries like Vietnam, India, Pakistan, and Mexico, just to name a few. However, only 40 to 50 years ago, clothes were created here in the United States. It was common for people to seek employment creating clothes. Well, the trend of creating clothes in the United States is slowly on the rise. The opening of boutiques and American clothes designers have stressed creating unique and cutting edge fashion, but also not to mass produce clothing—and this idea of creating clothes in the United States has reinvented itself. Why do you think clothing began being made in other countries? Do you think the United States will one day become a clothing creating © 2011 Carnegie Learning
powerhouse that it once was?
2.5 Using Tables, Graphs, and Equations, Part 1 • 91
7719_CL_C3_CH02_pp041-126.indd 91
13/03/14 10:19 AM
Problem 1 Cost Analysis This past summer you were hired to work at a custom T-shirt shop, U.S. Shirts. One of your responsibilities is to calculate the total cost of customers’ orders. The shop charges $8 per shirt plus a one-time charge of $15 to set up a T-shirt design. 1. Describe the problem situation and your responsibility in your own words.
2. What is the total cost of an order for: a. 3 shirts?
If the order doubles, does the total cost double?
Your answers should include the number of shirts and the total cost.
b. 10 shirts?
c. 100 shirts?
4. How many shirts can a customer buy if they have: a. $50 to spend?
92 • Chapter 2 Linear Functions
© 2011 Carnegie Learning
3. Explain how you calculated each total cost.
b. $60 to spend?
What operations do you need to perform to answer each? c. $220 to spend?
5. Explain how you calculated the number of shirts that each customer can buy.
6. Complete the table of values for the problem situation. Total Cost (dollars)
© 2011 Carnegie Learning
Number of Shirts Ordered
2.5 Using Tables, Graphs, and Equations, Part 1 • 93
7. What are the variable quantities in this problem situation? Define the variables that can represent these quantities including each quantity’s units.
Variable quantities are quantities that change, and constant quantities are quantities that don't change.
8. What are the constant quantities in this problem situation? Include the units that are used to measure these quantities.
9. Which variable quantity depends on the other variable quantity?
10. Which of the variables from Question 7 is the independent variable,
© 2011 Carnegie Learning
and which is the dependent variable?
94 • Chapter 2 Linear Functions
11. Create a graph of the data from your table in Question 6 on the grid shown. First, choose your bounds and intervals by completing the table shown. Remember to label your graph clearly and name your graph. Variable Quantity
Lower Bound
Upper Bound
Interval
Number of shirts Total cost
Consider all the data values when choosing your lower and upper bounds.
12. Draw a line to model the relationship between the number of shirts and the total cost of the shirts.
© 2011 Carnegie Learning
13. Do all the points on the line make sense in terms of this problem situation? Why or why not?
Use variables that make sense to you in terms of the problem situation.
14. Define the variables and write an algebraic equation for the problem situation.
2.5 Using Tables, Graphs, and Equations, Part 1 • 95
15. Define the domain and range for this problem situation.
Talk the Talk So far in this chapter, you have represented problem situations in four different ways: as a sentence, as a table, as a graph, and as an equation. 1. Complete the graphic organizer to explain the advantages and disadvantages of each representation.
Also think about the types of questions you can answer using each representation. © 2011 Carnegie Learning
Think about the type of information each representation displays.
Be prepared to share your solutions and methods.
96 • Chapter 2 Linear Functions
Table
Sentence Advantages
Advantages
Disadvantages
Disadvantages
Multiple Representations Advantages
Advantages
Disadvantages
© 2011 Carnegie Learning
Disadvantages
Graph
Equation
2.5 Using Tables, Graphs, and Equations, Part 1 • 97
© 2011 Carnegie Learning
98 • Chapter 2 Linear Functions
Learning Goals In this lesson, you will:
Use different models to represent a problem situation. Determine an initial value when given a final result. Identify the advantages and disadvantages of using a particular representation.
H
ave you ever wondered where your clothes come from? Who actually makes
the clothes you wear? For the most part, clothes are made in countries like Vietnam, India, Pakistan, and Mexico, just to name a few. However, only 40 to 50 years ago, clothes were created here in the United States. It was common for people to seek employment creating clothes. Well, the trend of creating clothes in the United States is slowly on the rise. The opening of boutiques and American clothes designers have stressed creating unique and cutting edge fashion, but also not to mass produce clothing—and this idea of creating clothes in the United States has reinvented itself. Why do you think clothing began being made in other countries? Do you think the United States will one day become a clothing creating © 2011 Carnegie Learning
powerhouse that it once was?
2.5 Using Tables, Graphs, and Equations, Part 1 • 91
7719_CL_C3_CH02_pp041-126.indd 91
13/03/14 10:19 AM
Problem 1 Cost Analysis This past summer you were hired to work at a custom T-shirt shop, U.S. Shirts. One of your responsibilities is to calculate the total cost of customers’ orders. The shop charges $8 per shirt plus a one-time charge of $15 to set up a T-shirt design. 1. Describe the problem situation and your responsibility in your own words.
2. What is the total cost of an order for: a. 3 shirts?
If the order doubles, does the total cost double?
Your answers should include the number of shirts and the total cost.
b. 10 shirts?
c. 100 shirts?
4. How many shirts can a customer buy if they have: a. $50 to spend?
92 • Chapter 2 Linear Functions
© 2011 Carnegie Learning
3. Explain how you calculated each total cost.
b. $60 to spend?
What operations do you need to perform to answer each? c. $220 to spend?
5. Explain how you calculated the number of shirts that each customer can buy.
6. Complete the table of values for the problem situation. Total Cost (dollars)
© 2011 Carnegie Learning
Number of Shirts Ordered
2.5 Using Tables, Graphs, and Equations, Part 1 • 93
7. What are the variable quantities in this problem situation? Define the variables that can represent these quantities including each quantity’s units.
Variable quantities are quantities that change, and constant quantities are quantities that don't change.
8. What are the constant quantities in this problem situation? Include the units that are used to measure these quantities.
9. Which variable quantity depends on the other variable quantity?
10. Which of the variables from Question 7 is the independent variable,
© 2011 Carnegie Learning
and which is the dependent variable?
94 • Chapter 2 Linear Functions
11. Create a graph of the data from your table in Question 6 on the grid shown. First, choose your bounds and intervals by completing the table shown. Remember to label your graph clearly and name your graph. Variable Quantity
Lower Bound
Upper Bound
Interval
Number of shirts Total cost
Consider all the data values when choosing your lower and upper bounds.
12. Draw a line to model the relationship between the number of shirts and the total cost of the shirts.
© 2011 Carnegie Learning
13. Do all the points on the line make sense in terms of this problem situation? Why or why not?
Use variables that make sense to you in terms of the problem situation.
14. Define the variables and write an algebraic equation for the problem situation.
2.5 Using Tables, Graphs, and Equations, Part 1 • 95
15. Define the domain and range for this problem situation.
Talk the Talk So far in this chapter, you have represented problem situations in four different ways: as a sentence, as a table, as a graph, and as an equation. 1. Complete the graphic organizer to explain the advantages and disadvantages of each representation.
Also think about the types of questions you can answer using each representation. © 2011 Carnegie Learning
Think about the type of information each representation displays.
Be prepared to share your solutions and methods.
96 • Chapter 2 Linear Functions
Table
Sentence Advantages
Advantages
Disadvantages
Disadvantages
Multiple Representations Advantages
Advantages
Disadvantages
© 2011 Carnegie Learning
Disadvantages
Graph
Equation
2.5 Using Tables, Graphs, and Equations, Part 1 • 97
© 2011 Carnegie Learning
98 • Chapter 2 Linear Functions
