Lesson 7.1 Assignment

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1 Lesson 7.1 Assignment Name Date Picture This Picture Algebra 1. The Sharks Aquatic Club recently held a fundraiser to raise money for a local charity. The swimmers received money for each lap that they swam during a one-week period. The three swimmers who raised the most money were Rita, John, and Rodell. Together they swam a total of 2125 laps. John swam three times as many laps as Rita, and Rodell swam 25 more laps than John. How many laps did each swimmer swim? a. Draw a picture to represent the situation. Label the unknown parts with variables and the known parts with their values. Rita: John: Rodell: b. Determine the number of laps each person swam using the picture you created. Explain your reasoning. Chapter 7 Assignments 121

2 Lesson 7.1 Assignment page 2 c. Write an expression for the number of laps each person swam. Let L represent the number of laps swum by Rita. The number of laps swum by Rita: The number of laps swum by John: The number of laps swum by Rodell: d. Write an equation to represent this situation. e. If the swimmers received $2 for every lap they swam, how much did each swimmer earn for charity? 122 Chapter 7 Assignments

3 Lesson 7.2 Assignment Name Date Maintaining a Balance Solving Equations 1. Madison Middle School has a Math and Science Club that holds meetings after school. The club has decided to enter a two-day competition that involves different math and science challenges. The first day of competition involves solving multi-step math problems. Teams will receive one point for every problem they get correct. Halfway through the day, the Madison Middle School Team has 4 points. After a dinner break, the team does more problems and is able to finish the day with 11 points. a. The representation shows a balance for this situation. The left side of the balance represents the 4 points the team had at midday plus the additional points they got after dinner. The right side of the balance represents the total points they had at the end of the day. What will balance 1 rectangle in this representation? Describe your strategy. Strategy: What will balance 1 rectangle? How many problems did they get correct after dinner? b. Rewrite the representation from part (a) using symbols. Let 5 x and 5 1 point. Then describe how the strategies you used to determine what balanced 1 rectangle can apply to the equation. Chapter 7 Assignments 123

4 Lesson 7.2 Assignment page 2 c. Does the value of x maintain balance in the original equation? Substitute the value of x back into the original equation to check. Show your work. d. What does the value x 5 7 mean in the original situation? 2. The second day of a math and science competition involves all hands-on science problems. Because of the complexity of the problems, each team will get 3 points for every science problem that they get correct. The Madison Middle School team is starting the day with 11 points. By the end of the day the team had 23 points. a. The representation shows a balance for this situation. The left side of the balance represents the 11 points the team had at the start of the day plus the additional points they got from the science competition. The right side of the balance represents the total points they had at the end of the second day. What will balance 1 rectangle in this representation? Describe your strategy. Strategy: 124 Chapter 7 Assignments

5 Lesson 7.2 Assignment page 3 Name Date What will balance 1 rectangle? How many science problems did they get correct? b. Rewrite the representation from part (a) using symbols. Let 5 x and 5 1 point. c. Solve the equation from part (b). Write a sentence to describe how to apply inverse operations to solve the equation. Then, solve the equation. Chapter 7 Assignments 125

6 Lesson 7.2 Assignment page 4 d. Does the value of x that you got as your solution maintain balance in the original equation? Substitute the value of x back into the original equation to check. Show your work. 126 Chapter 7 Assignments

7 Lesson 7.3 Assignment Name Date Planning a Graduation Party Solving Two-Step Equations 1. Employees at Driscoll s Electronics earn a base salary plus a 20% commission on their total sales for the year. The employees base salaries differ depending on how long they have been employed. The owner of Driscoll s gets a report each year that shows the amount each employee who has been there for more than one year earned. a. Complete the table. Employee Base Salary (dollars) Amount of Sales (dollars) Total Salary (dollars) Jones 30,000 75,000 Padilla 35,000 95,000 Stewart 37,000 58,000 Freese 42,000 60,000 Gross 150,000 75,000 Lin 180,000 77,000 b. Write an equation to represent this situation. Define your variables. Chapter 7 Assignments 127

8 Lesson 7.3 Assignment page 2 c. The owner decides to give everyone a raise on their base salary. Stewart s base salary increases to $40,000. How much must he make in sales if he wants his total salary to be $65,000? Use your equation and write a sentence to describe how to apply inverse operations to solve it. d. Verify your solution. Explain your reasoning. 128 Chapter 7 Assignments

9 Lesson 7.3 Assignment page 3 Name Date e. The owner also gets a report on the salaries made by new employees. Each new employee gets a base salary of $20,000 and 10% commission on their total yearly sales. Write an equation to represent the total salary for new employees. f. Hodges, a new employee, had a total salary of $30,000 for the year. Use the equation to determine how much he made in sales. Write a sentence to describe how to apply inverse operations to solve it. Verify your solution. Chapter 7 Assignments 129

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11 Lesson 7.4 Assignment Name Date Solving in Big-Time Style Using Two-Step Equations 1. Drake s Drugstore is getting ready for the upcoming summer season. The manager of the store wants to add lawn chairs to the stock. He asks the buyer to determine the two lowest priced wholesalers of lawn chairs. The table shows the data that the buyer collects from two wholesalers. Packs of Chairs Price from Wholesaler A (dollars) Price from Wholesaler B (dollars) 1 $90.99 $ $ $ $ $ $ $ Use the table to answer each question. a. At Wholesaler A, what is the difference in price between two packs of chairs and one pack of chairs? What is the difference in price between four packs of chairs and three packs of chairs? b. How does the total cost of buying chairs from Wholesaler A change when the number of packs of chairs increases by one pack (except the first pack)? Chapter 7 Assignments 131

12 Lesson 7.4 Assignment page 2 c. Let p represent the total number of packs of chairs bought from Wholesaler A. Write an expression to calculate any number of packs of chairs. Explain your reasoning. d. Simplify your expression. e. Use your expression to determine what it would cost to buy eight packs of chairs from Wholesaler A? Explain your reasoning. f. Use your expression to determine the number of packs of chairs the drugstore bought from Wholesaler A if the cost is $ Chapter 7 Assignments

13 Lesson 7.4 Assignment page 3 Name Date g. What is the cost to buy one pack of chairs from Wholesaler B? h. At Wholesaler B, what is the difference in price between two packs of chairs and one pack of chairs? What is the difference in price between four packs of chairs and three packs of chairs? i. Let p represent the total number of packs of chairs bought from Wholesaler B. Write an expression to calculate any number of packs of chairs. Explain your reasoning. Remember to simplify your expression. j. Use your expression to determine what it would cost to buy eight packs of chairs from Wholesaler B? Explain your reasoning. Chapter 7 Assignments 133

14 Lesson 7.4 Assignment page 4 k. At how many packs of chairs will the price to buy them from Wholesaler A by the same as the price to buy them from Wholesaler B? Write an equation and explain your reasoning. l. The manager wants to buy at least seven packs of chairs. Which wholesaler should the drugstore use this year? Explain your reasoning. 134 Chapter 7 Assignments

15 Lesson 7.4 Assignment page 5 Name Date 2. The manager of a home store is buying lawn chairs to sell at his store. Each pack of chairs contains 10 chairs. The manager will sell each chair at a markup of 20% of the wholesale cost, plus a $2.50 stocking fee. a. Write an equation that represents the retail price of a chair, r, in terms of the wholesale price, w. b. Use your equation to calculate the retail price of the chair if the wholesale price is $8.40. c. Use your equation to calculate the retail price of the chair if the wholesale price is $8.55. d. Use your equation to calculate the wholesale price of the chair if the retail price is $ Chapter 7 Assignments 135

16 Lesson 7.4 Assignment page 6 e. Use your equation to calculate the wholesale price of the chair if the retail price is $ Chapter 7 Assignments

17 Lesson 7.5 Assignment Name Date We re Shipping Out! Solving and Graphing Inequalities in One Variable 1. Taneisha has decided to go on a new cell phone plan. She makes $150 per month babysitting so she has to be careful of how much she spends on the plan. a. If the plan costs $55 per month plus $0.20 for each text, write and solve the inequality to determine the maximum number of texts she can make and still afford to pay the bill. b. What is the least amount of texts Taneisha can make? c. Graph the solution set for the number of texts Taneisha can make in one month. Chapter 7 Assignments 137

18 Lesson 7.5 Assignment page 2 d. Choose a value from the solution set and verify that it is a solution. 2. Taneisha has found a different cell phone plan that she thinks might be better for her. This plan charges $90 plus $0.15 for every text over 100. Write an expression to represent the monthly cost of this plan. a. Simplify the expression for the cost of this plan. b. Taneisha wants to determine the number of texts for which the cost of this plan is less than the cost of the original plan. Write the inequality for this situation and solve. 138 Chapter 7 Assignments