Prepping for the Robot Challenge

Transcription

1 Lesson.1 Assignment Name Date Prepping for the Robot Challenge Solving Linear Systems Graphically and Algebraically 1. Wesley owns a dairy farm. In the morning, it takes him 0.3 hour to set up for milking the cows. Once he has set up, it takes Wesley 0.2 hour to milk each cow by hand. He is contemplating purchasing a milking machine in hopes that it will speed up the milking process. The milking machine he is considering will take 0.4 hour to set up each morning and takes 0.05 hour to milk each cow. a. Write a system of linear equations that represents the total amount of time Wesley will spend milking the cows using the two different methods. b. Compare the equations in the system you wrote in part (a). Explain what they mean in terms of the problem situation. c. Graph both equations on the coordinate plane. y Total Time for Milking (hours) Number of Cows x Chapter Assignments 77

2 Lesson.1 Assignment page 2 d. Use the graph to estimate the break-even point. Explain how you determined your answer. e. What does the break-even point represent in this problem situation? f. Verify your answer to part (d) by solving the system algebraically. g. Does the solution make sense in terms of this problem situation? Explain your reasoning. h. Which method of milking is more efficient? Explain your reasoning. i. Is this system of equations consistent or inconsistent? Explain your reasoning. 78 Chapter Assignments

3 Lesson.2 Assignment Name Date There s Another Way? Using Linear Combinations to Solve a Linear System 1. The two high schools in the Jefferson Hills School District are named Jefferson Hills East and Jefferson Hills West. Both schools are taking field trips to the state capital. A total of 408 students from Jefferson Hills East will be going in 3 vans and buses. A total of 51 students from Jefferson Hills West will be going in vans and 7 buses. Each van has the same number of passengers and each bus has the same number of passengers. a. Write an equation in standard form that represents the students from Jefferson Hills East. Let x represent the number of students in each van, and let y represent the number of students in each bus. b. Write an equation in standard form that represents the students from Jefferson Hills West. Use the same variables as those used in part (a). c. How are the equations in parts (a) and (b) the same? How are they different? d. Describe the first step needed to solve the system using the linear combinations method. Identify the variable that will be eliminated as well as the variable that will be solved for when you add the equations. Chapter Assignments 79

4 Lesson.2 Assignment page 2 e. Use your answer from part (d) to solve for one of the variables in the linear system of equations. Then solve for the other variable. Show your work. f. What is the solution of the linear system? Interpret the solution of the linear system in terms of the problem situation. g. Check your solution algebraically. 80 Chapter Assignments

5 Lesson.3 Assignment Name Date What s For Lunch? Solving More Systems 1. Rika works in the perfume department at Hoover s Department Store. She is giving away samples of a new fragrance and a new scented hand lotion to customers that pass by her station. She is required to hand out a total of 114 samples during her shift. She has already handed out 3 samples, which represents 1 3 of the number of fragrance samples and 1 of the number of 4 hand lotion samples that she must hand out. a. Write an equation in standard form to represent the total number of samples that she must hand out. Let x represent the number of fragrance samples and let y represent the number of hand lotion samples. b. Write an equation in standard form to represent the number of samples that Rika has handed out so far. Use the same variables as those used in part (a). c. Write a system of linear equations that represents the problem situation. d. Rewrite the equation containing fractions as an equivalent equation without fractions. Show your work. Chapter Assignments 81

6 Lesson.3 Assignment page 2 e. Determine the solution of the system of equations using linear combinations. Check your answer. f. Interpret the solution of the linear system in terms of the problem situation. 82 Chapter Assignments

7 Lesson.3 Assignment page 3 Name Date 2. Belinda works in the kitchen department of Hoover s Department Store. As part of the store s effort to reward their customers, Belinda will be handing out coupons for two different types of silverware packages. The first coupon is for the classic set, and the second coupon is for the modern set. On one particular day, she hands out a total of 144 coupons, which represents 1 of the number 2 of classic set coupons and 3 of the number of modern set coupons. She hands out twice as many 4 coupons for the modern set as she does for the classic set. a. Write an equation in standard form to represent the total number of coupons Belinda has handed out so far. Let x represent the number of coupons for the classic set and let y represent the number of coupons for the modern set. b. Write an equation in standard form that represents the relationship between the numbers of coupons she hands out for each set of silverware. Use the same variables as those used in part (a). c. Write the system of linear equations that represents the problem situation. Chapter Assignments 83

8 Lesson.3 Assignment page 4 d. Solve the linear system of equations using linear combinations. e. Interpret the solution of the linear system in terms of the problem situation. 84 Chapter Assignments

9 Lesson.4 Assignment Name Date Which Is the Best Method? Using Graphing, Substitution, and Linear Combinations 1. Antonio wants to subscribe to a service that will allow him to rent DVDs and stream movies online. Movie Madness offers a subscription for $14.25 a month. With this subscription, Antonio will receive one DVD at a time and can check out as many DVDs as he wants each month. However, he must pay $1.40 for each movie he streams online. The Show Must Go On! offers a subscription for $8.50 a month. With this subscription, Antonio will receive one DVD at a time and can checkout as many DVDs as he wants each month. However, he must pay $3.25 for each movie he streams online. a. Write a system of linear equations to represent this problem situation. b. Without actually analyzing this system, make a prediction about which subscription plan will be the better deal. Explain your reasoning. c. Analyze the two subscription plans and determine which one is the better deal. Use any or all of the methods you have learned in Chapter to determine your answer. Chapter Assignments 85

10 Lesson.4 Assignment page 2 d. Write a short paragraph recommending which subscription Antonio should choose. e. Which method do you think provides the quickest way to analyze a system of equations to determine which one is the better deal? Explain your reasoning. 8 Chapter Assignments