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MAT/116
Algebra 1A
Version 7 01/01/2010
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Faculty Materials
BOOKS, SOFTWARE, OR OTHER COURSE MATERIALS
BITTENGER, M. L., & BEECHER, J. A. (2007). INTRODUCTORY AND INTERMEDIATE ALGEBRA (3RD ED.). BOSTON, MA: PEARSON/ADDISON WESLEY.
ELECTRONIC RESOURCES
FOR THIS COURSE, STUDENTS AND FACULTY ARE REQUIRED TO USE MYMATHLAB®, WHICH CAN BE ACCESSED THROUGH THE STUDENT AND FACULTY WEBSITES.
Faculty materials associated with the textbook may be accessed at .
Login name: uopinstructor
Password: uopinstructor
Note. Do not share this login information with students.
Associate Level MATERIALS
ASSOCIATE LEVEL WRITING STYLE HANDBOOK, AVAILABLE ONLINE AT
Course Overview
COURSE DESCRIPTION
THIS COURSE INTRODUCES BASIC ALGEBRA CONCEPTS AND ASSISTS IN BUILDING SKILLS FOR PERFORMING SPECIFIC MATHEMATICAL OPERATIONS AND PROBLEM SOLVING. STUDENTS SOLVE EQUATIONS, EVALUATE ALGEBRAIC EXPRESSIONS, SOLVE AND GRAPH LINEAR EQUATIONS AND LINEAR INEQUALITIES, GRAPH LINES, AND SOLVE SYSTEMS OF LINEAR EQUATIONS AND LINEAR INEQUALITIES. THESE CONCEPTS AND SKILLS SERVE AS A FOUNDATION FOR SUBSEQUENT COURSEWORK. APPLICATIONS TO REAL-WORLD PROBLEMS ARE INTEGRATED THROUGHOUT THE COURSE. THIS COURSE IS THE FIRST HALF OF THE COLLEGE ALGEBRA SEQUENCE, WHICH IS COMPLETED IN ALGEBRA 1B.
Topics and Objectives
WEEK ONE: REAL NUMBERS AND ALGEBRAIC EXPRESSIONS
• Compare the values of integers.
• Simplify expressions using the order of operations and properties of real numbers.
• Translate phrases into mathematical expressions.
• Use substitution to evaluate algebraic expressions.
Week Two: Solving Algebraic Equations and Inequalities
• Solve one-variable equations using the addition and multiplication principles.
• Determine whether a given point is a solution for a linear equation.
• Solve a formula for a variable.
Week Three: More on Solving Equations and Inequalities
• Solve one-variable inequalities using the addition and multiplication principles.
• Graph one-variable inequalities.
• Determine whether a given point is a solution for a linear inequality.
• Translate sentences into inequalities.
Week Four: Graphing Linear Equations
• Graph points from ordered pairs in an (x,y) coordinate system.
• Determine whether a given point is a solution for a linear equation.
• Graph a linear equation using tables and intercepts.
• Find the slope of a line given two points or the equation of a line.
Week Five: Functions
• Differentiate between functions and equations.
• Find function values for specific domain values.
• Determine the domain and range of a function.
Week Six: Graphs of Functions
• Graph linear equations using slope and y-intercepts, or x- and y-intercepts.
• Determine whether lines are perpendicular, parallel, or intersecting.
• Write linear equations using point-slope and y-intercept forms.
Week Seven: Systems of Equations
• Solve systems of linear equations using graphing and methods of substitution and elimination.
• Determine whether a system is consistent or inconsistent.
• Determine whether equations of a system are dependent or independent.
Week Eight: Systems of Inequalities
• Solve and graph systems of inequalities in one and two variables.
Week Nine: Apply Algebraic Concepts
• Apply algebraic concepts to solve mathematical problems.
Week One Faculty Notes
Topics and Objectives
REAL NUMBERS AND ALGEBRAIC EXPRESSIONS
• Compare the values of integers.
• Simplify expressions using the order of operations and properties of real numbers.
• Translate phrases into mathematical expressions.
• Use substitution to evaluate algebraic expressions.
Weekly Overview
This week, students begin learning the fundamental skills of algebra. Students learn the language of algebra so they can apply algebra to real life situations. Students learn the importance of using the order of operations in mathematics. Students begin working with MyMathLab® and may need additional support as they get used to a new environment.
Assignment Notes
Discussion Questions are due this week.
CheckPoint: Algebraic Expressions
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. In MyMathLab®, you can check students’ scores, review student work, and manage student performance. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Two Faculty Notes
Topics and Objectives
SOLVING ALGEBRAIC EQUATIONS AND INEQUALITIES
• Solve one-variable equations using the addition and multiplication principles.
• Determine whether a given point is a solution for a linear equation.
• Solve a formula for a variable.
Weekly Overview
Students learn procedures required to correctly solve linear equations. Students also learn to manipulate formulas to solve for a variable. Students explore mathematical concepts in the context of owning a business. A formal assessment at the end of the week determines student understanding of concepts presented in Weeks One and Two.
Assignment Notes
CheckPoint: Linear Equations
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Exercises are due this week.
Assignment: Expressions and Equations
Purpose of Assignment
Part 1 of the assignment provides students the opportunity to explore mathematical concepts addressed in Weeks One and Two in the context of owning a bakery. Students demonstrate their understanding of evaluating expressions and solving equations through their writing. Part 2 of the assignment assesses students’ conceptual and procedural knowledge of mathematical concepts learned in Weeks One and Two. Students use MyMathLab® to complete this assessment.
Resources Required
Appendix C
MyMathLab®
Answer Key for Expressions and Equations: Part 1, Due in Week Two
Answers to Appendix C are provided in red below. The answer key is provided as a grading guideline only; there may be many ways to arrive at a correct answer. Please use your professional judgment when assessing student work.
Application Practice
Answer the following questions. If appropriate, use Equation Editor to show your work. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
1. You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an $80,000 loan from your family, and a $38,250 small business loan. These loans must be repaid in full within 10 years.
a. What integer would represent your total budget?
$118,250
b. You will use 25% of your budget to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not solve.
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c. How much money will rent and utilities cost? Explain how you arrived at this answer.
$29,562.50. Student responses may vary. Possible explanation: 0.25 is the decimal equivalent of 25%. The answer can be obtained by multiplying $118,250, the answer to part a, by 0.25.
d. Imagine an investor has increased your budget by $22,500. The investor does not need to be repaid. Rather, he becomes part owner of your business. Will the investor contribute enough money to meet the costs of rent and utilities? Support your answer, and write an equation or inequality that illustrates your answer.
No, the investor did not contribute enough money to pay for the rent and utilities. These costs total $29,562.50 (answer to part c). Since $29,562.50>$22,500, the investor did not meet these needs.
e. This equation illustrates your remaining funds after paying for rent and utilities. How much money is left? Explain how you arrived at your answer.
$38,250 + $80,000+ $22,250-0.25($80,000 + $38,250) = $110,937.50
2. You are trying to decide how to most efficiently use your oven. You do not want the oven running at a high temperature when you are not baking, but you also do not want to waste a lot of time waiting for the oven to reach the desired baking temperature.
The instruction manual on the industrial oven suggests the oven temperature will increase by 45 degrees Fahrenheit per minute. When the oven is turned off, the temperature is 70 degrees Fahrenheit. What will the temperature of the oven be after 7 minutes? Write an expression and explain how you arrived at your answer.
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The oven will reach 385 degrees after 7 minutes. Substitute 7 for x in the expression. First, multiply 45 by 7 and then add 70.
3. Your industrial oven can bake two baking sheets with 12 scones each, two baking sheets with 20 cookies each, and one baking sheet with two scones and 10 cookies.
a. Write an expression that illustrates the scenario above using the variable s to represent scones, and the variable c to represent cookies. Simplify your expression by combining like terms.
[pic]
This expression can be simplified to:
[pic]
b. Imagine you have decided to price the scones at $2.28 each and the cookies at $1.19 each. How much total revenue would result from selling all the scones and cookies baked in the oven at one time?
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c. Yesterday, your store earned $797.30 just from the sale of cookies. Write and solve an equation that represents how many cookies were sold.
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c = 670
4. Your profit P is determined by subtracting the cost C, the amount of money it costs to operate a business, from the revenue R, the amount of money you earn from selling your product. Profit can be represented algebraically by the equation:
Profit = Revenue - Cost
OR
P = R - C
a. Rewrite the formula to solve for C.
C = R - P
b. Imagine your profit for 1 day is $1,281, and the cost of running the business for the day is $1,463. What was the revenue for that day? Explain your answer.
[pic]
R = $2,744. By substituting $1,281 for P and $1,463 for C, the equation can be solved by adding $1,463 to $1,281.
5. When managing a business, it is important to take inventory of where your money is spent. You have a monthly budget of $5,000. Refer to the table below and answer the questions that follow. Round your answers to the nearest tenth of a percent.
|Category |Cost |Percentage |
|Labor |$1,835 | |
|Materials | |18% |
|Rent and utilities | |25% |
|Miscellaneous |$1,015 | |
|Total |$5,000 |100% |
a. What percentage of the total monthly budget is spent on labor?
36.7% of the total monthly budget is spent on labor.
b. What percentage of the total monthly budget is spent on miscellaneous items?
20.3% of the total monthly budget is spent on miscellaneous items.
c. How much do materials cost monthly?
Materials for the month cost $900.
d. How much do rent and utilities cost monthly?
Monthly rent and utilities cost $1,250.
Grading Guide for Expressions and Equations: Part 2, Due in Week Two
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Three Faculty Notes
Topics and Objectives
MORE ON SOLVING EQUATIONS AND INEQUALITIES
• Solve one-variable inequalities using the addition and multiplication principles.
• Graph one-variable inequalities.
• Determine whether a given point is a solution for a linear inequality.
• Translate sentences into inequalities.
Weekly Overview
This week, students learn to solve and graph one-variable equations. In order to do this, they must apply many of the same techniques they learned when solving equations. Again, students use MyMathLab® to practice skills related to solving inequalities.
Assignment Notes
Discussion Questions are due this week.
CheckPoint: Solving Inequalities
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Four Faculty Notes
Topics and Objectives
GRAPHING LINEAR EQUATIONS
• Graph points from ordered pairs in an (x,y) coordinate system.
• Determine whether a given point is a solution for a linear equation.
• Graph a linear equation using tables and intercepts.
• Find the slope of a line given two points or the equation of a line.
Weekly Overview
This week introduces students to the Cartesian coordinate system. Students practice their new skills using MyMathLab®. Students apply graphing skills in the context of a do-it-yourself landscaping project. Students end the week with a MyMathLab® quiz that assesses content from Weeks Three and Four.
Assignment Notes
CheckPoint: Graphing Equations
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Exercises are due this week.
Assignment: Solving Inequalities and Graphing Equations
Purpose of Assignment
Part 1 of the assignment allows students to apply skills from Ch. 2 & 3 to a real life situation. Students assume the role of a do-it-yourself landscaper. Within this context, students apply skills of solving inequalities, determining slope, and graphing points and equations in the coordinate plane. Part 2 of the assignment is a quiz that assesses students’ conceptual and procedural knowledge of mathematical concepts learned in Ch. 2 & 3. Students use MyMathLab® to complete this part of the assignment.
Resources Required
Appendix D
MyMathLab®
Answer Key for Solving Inequalities and Graphing Equations: Part 1, Due in Week Four
Answers to Appendix D are provided in red below. The answer key is provided as a grading guideline only; there may be many ways to arrive at a correct answer. Please use your professional judgment when assessing student work.
Application Practice
Answer the following questions. If appropriate, use Equation Editor to show your work. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.
a. Write an inequality that demonstrates how much money you are willing to spend on the project.
[pic]
b. For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
[pic]
To solve this problem, multiply 60 by 30. This answer indicates how much the rock will cost, which is $1,800. Subtract $1,800 from $2,500 to arrive at $700. This means you have $700 to spend on trees. Divide $700 by the cost of each tree, which is $84. The answer, 8.3333…, indicates how many trees you can buy. Since you cannot buy a portion of a tree and do not have enough money to buy 9 trees, you can purchase a maximum of 8 trees.
c. Would five trees be a solution to the inequality in Part b? Justify your answer.
Yes. The number 5 is less than or equal to 8. The cost of 5 trees is also less than the cost of 8, so you are still under budget.
2. The coordinate graph of the backyard shows the location of the trees, plants, patio, and utility lines. If necessary, you may copy and paste the image to another document and enlarge it.
a. What are the coordinates of Tree A, Plant B, Plant C, Patio D, Plant E, and Plant F?
Tree A (-20,20); Plant B (-20,-4); Plant C (-10,-14); Patio D (12,12), Plant E (8,-8); Plant F (18,-12)
b. The water line is given by the equation
[pic]
Imagine you want to put a pink flamingo lawn ornament in your backyard. You want to avoid placing it directly over the water line in case you need to excavate the line for repairs in the future. Could you place it at point (-4, -10)?
Yes, it would not lie directly on the line, but it would be close to the water line. Some students may argue that this may not be the best choice for the ornament, but they should determine that (-4, -10) is not a solution.
c. What is the slope and y-intercept of the line in Part b? How do you know?
[pic] [pic]
The slope is the rate of change; It indicates how much the y will increase as x increases. The intercept b indicates the value of the line when x = 0.
d. Imagine you want to add a sprinkler system and the location of one section of the sprinkler line can be described by the equation
[pic]
Complete the table for this equation.
|x |y |(x,y) |
|-6 |-1 |(-6, -1) |
|-2 |-3 |(-2, -3) |
|0 |-4 |(0, -4) |
|2 |-5 |(2, -5) |
|8 |-8 |(8, -8) |
e. What objects might be in the way as you lay the pipe for the sprinkler?
Plant E lies on the line and will be an obstacle. Plant F, while not a solution, is close enough to the line that it may be a problem.
Grading Guide for Solving Inequalities and Graphing Equations: Part 2, Due in Week Four
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Five Faculty Notes
Topics and Objectives
FUNCTIONS
• Differentiate between functions and equations.
• Find function values for specific domain values.
• Determine the domain and range of a function.
Weekly Overview
This week, students explore the definition of functions and practice determining the domain and range of a function. Students also discover how functions can be used to model many real life situations. Students use MyMathLab® to practice skills introduced this week.
Assignment Notes
Discussion Questions are due this week.
CheckPoint: Introduction to Functions
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Six Faculty Notes
Topics and Objectives
GRAPHS OF FUNCTIONS
• Graph linear equations using slope and y-intercepts, or x- and y-intercepts.
• Determine whether lines are perpendicular, parallel, or intersecting.
• Write linear equations using point-slope and y-intercept forms.
Weekly Overview
This week, students expand on their conceptual knowledge from previous weeks and begin graphing linear equations using a variety of methods. Students begin working with sets of lines in a coordinate graph. This introduction prepares students for systems of equations in future weeks.
Assignment Notes
CheckPoint: Looking at Functions
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Exercises are due this week.
Assignment: Functions and Their Graphs
Purpose of Assignment
The first part of the assignment requires students to apply skills from Ch. 7 to a real life situation. In this activity, students analyze the effects of rising gasoline prices. Students use data to make predictions and answer relevant questions using mathematical concepts. Within this context, students determine an appropriate domain and range and graph linear functions. In the second part of the assignment, students complete a quiz that assesses students’ conceptual and procedural knowledge of mathematical concepts learned in Ch. 7. Students use MyMathLab® to complete this assessment.
Resource Required
Appendix E
MyMathLab®
Answer Key for Functions and their Graphs: Part 1, Due in Week Six
Answers to Appendix E are provided in red below. The answer key is provided as a grading guideline only; there may be many ways to arrive at a correct answer. Please use your professional judgment when assessing student work.
Application Practice
Answer the following questions. If appropriate, use Equation Editor to show your work. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
1. Imagine you are at a gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons of regular gasoline. Given the equation
[pic]
a. What does the number 3.03 represent?
The value 3.03 represents the cost per gallon of gas.
b. Find C(2).
$6.06
c. Find C(9).
$27.27
d. For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose that number.
Student answers may vary. A possible example: 100 is inappropriate because the typical motorist will not have a 100-gallon tank.
e. If you were to graph C(g), what would be an appropriate domain and range? Explain your reasoning.
Student answers may vary. All answers should include 0 as the minimum number in the domain and range. One possible answer:
[pic][pic]
2. Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26, and in January 2006, the price of regular unleaded gasoline was $2.31 (“Consumer price index,” 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope, or rate of change, between the two points. Describe how you arrived at your answer.
[pic]
To arrive at this answer, subtract the y-values from each of the coordinates and place the value of the difference in the numerator. Then subtract the x-values from each of the coordinates and place the difference in the denominator. Finally, simplify by dividing the numerator by the denominator.
3. The linear equation
[pic]
represents an estimate of the average cost of gas for year x, starting in 1997 (“Consumer price index,” 2006). The year 1997 would be represented by x = 1, for example, because it is the first year in the study. Similarly, 2005 would be year 9, or x = 9.
a. What year would be represented by x = 4?
2000
b. What x-value represents the year 2018?
x = 22
c. What is the slope, or rate of change, of this equation?
[pic]
d. What is the y-intercept?
[pic]
e. What does the y-intercept represent?
The y-intercept represents the average price of gas in 1996 (when x = 0).
f. Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer?
The price of gasoline in 2018 will be $4.09 per gallon if the trend continues. This answer can be found by substituting the answer from Part a (x=22) for the x value in the equation.
[pic]
4. The line
[pic]
represents an estimate of the average cost of gasoline each year. The line
[pic]
estimates the price of gasoline in January of each year (“Consumer price index,” 2006).
a. Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning.
Student answers may vary. Students must support their answers with a logical reason. Students should not choose perpendicular.
b. Use the equations of the lines to determine if they are parallel. What did you find?
The slope of the first equation is 0.15 and the slope of the second equation is 0.11. Since the slopes are not equivalent, the lines are intersecting and not parallel.
c. Did your answer to Part b. confirm your expectation in Part a?
Student answers may vary.
References
Bureau of Labor Statistics. (2006). Consumer price index. Retrieved from
Grading Guide for Functions and their Graphs: Part 2, Due in Week Six
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Seven Faculty Notes
Topics and Objectives
SYSTEMS OF EQUATIONS
• Solve systems of linear equations using graphing and methods of substitution and elimination.
• Determine whether a system is consistent or inconsistent.
• Determine whether equations of a system are dependent or independent.
Weekly Overview
Students use different methods to determine the solution, or intersection point, of a pair of lines. Solving systems of equations is a skill that has many practical mathematical applications. Students have the opportunity to practice their skills in both theoretical and contextual settings. This week, students continue working in MyMathLab®.
Assignment Notes
Discussion Questions are due this week.
CheckPoint: Solving Systems of Equations
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Eight Faculty Notes
Topics and Objectives
SYSTEMS OF INEQUALITIES
• Solve and graph systems of inequalities in one and two variables.
Weekly Overview
This week, students further develop skills from Weeks Three and Seven as they begin to solve inequalities in one and two variables. Students assume the role of a home buyer as they explore systems of equations and inequalities.
Assignment Notes
CheckPoint: Solving Systems of Inequalities
Resource Required
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Exercises are due this week.
Assignment: Systems of Equations and Inequalities
Purpose of Assignment
This assignment provides a real life setting in which students can explore the concepts of systems of equations and inequalities. Students are responsible for deriving and solving systems of equations and inequalities. Students can use the skills learned in this lesson to make purchasing decisions in the future. The quiz in Part 2 of the assignment assesses students’ conceptual and procedural knowledge of mathematical concepts learned in Ch. 8 & 9. Students use MyMathLab® to complete this assessment.
Resources Required
Appendix F
MyMathLab®
Answer Key for Systems of Equations and Inequalities: Part 1, Due in Week Eight
Answers to Appendix F are provided in red below. The answer key is provided as a grading guideline only; there may be many ways to arrive at a correct answer. Please use your professional judgment when assessing student work.
Application Practice
Answer the following questions. If appropriate, use Equation Editor to show your work. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
1. Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city.
a. The sales representative informs you that there are 56 houses for sale with two floor plans still available . Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.
[pic]
b. The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part a.
[pic]
c. Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.
Substitute 3x for the y in the first equation. Doing this leaves 4x=56, so x=14. Then, substitute 14 for x in either equation to find that y=42. This means there are 14 homes with floor plan one and 42 homes with floor plan two.
d. What are the intercepts of the equation from Part a. of this problem? What are the intercepts from Part b. of this problem? Where would the lines intersect if you solved the system by graphing?
For the first equation, the intercepts are (56, 0) and (0,56). The intercept for the second equation is (0, 0). The lines would intersect at (14, 42).
2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.
a. The sales representative here tells you they also have two floor plans available, but they only have 38 homes still for sale. Write an equation that illustrates the situation. Use x and y to denote floor plan one and floor plan two respectively.
[pic]
b. The representative tells you that floor plan one sells for $175,000 and floor plan two sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in Part a.
[pic]
c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.
Students arrive at their answer by either multiplying the first equation by -175,000 or -200,000. This eliminates one variable. Students can then solve for the remaining variable and substitute it into the first equation to find the second variable. Students must arrive at the answer (16, 22). This means there are 16 available houses with floor plan one, and 22 available houses with floor plan two.
3. You recently started the paperwork to purchase your new home, and were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifting and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.
a. Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
Heavy Lifting would charge $150 for 2 hours and Quick Move would charge $110. For 2 hours of work, Quick Move would be the better company. To find the fee for Heavy Lifting, multiply the number of hours by the hourly rate and add the fee. To find the fee for Quick Move, multiply the number of hours by the hourly rate.
b. Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
For 15 hours of work, Heavy Lifting would charge $605 and Quick Move would charge $825. In this case, Heavy Lifting would be the better company.
c. For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer.
Students might use the method of guess and check or set up a system of equations. Quick Move offers the better deal for less than 4 hours. [pic]. When [pic], both companies offer the same deal. Neither is better.
Grading Guide for Systems of Equations and Inequalities: Part 2, Due in Week Eight
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
Week Nine Faculty Notes
Topics and Objectives
APPLY ALGEBRAIC CONCEPTS
• Apply algebraic concepts to solve mathematical problems.
Weekly Overview
This week, students complete a comprehensive Final Exam. The exam covers salient concepts of the course outlined by the course objectives. The exam assesses concepts introduced in Weeks One through Eight.
Assignment Notes
A Capstone Discussion Question is due this week.
Final Project: Final Exam
Purpose of Assignment
The comprehensive final exam assesses students’ conceptual and procedural knowledge of mathematical concepts learned in the first eight weeks of class. Students use MyMathLab® to complete this assessment.
Resources Required
Appendix A
MyMathLab®
Grading Guide
Students submit their work through MyMathLab®. Check that students complete their assignments by the due date. Deduct appropriate points from assignments submitted after the due date.
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