Lesson 1.1 Assignment Name Date A Park Ranger s Work Is Never Done Solving Problems Using Equations 1. Joyce is helping to make wreaths for her Women s Club to sell at a local bazaar. She will be making the bows for each wreath. She has 60 feet of ribbon to start. She needs 1 2 feet of ribbon for 3 each bow. a. How many feet of ribbon will Joyce have left if she makes 10 bows? b. How many feet of ribbon will Joyce have left if she makes 15 bows? c. Define a variable for the amount of bows that Joyce makes. Then use the variable to write an expression that represents the length of ribbon that Joyce has left, given the number of bows that she has made. d. How many bows has Joyce made if she has 10 feet of ribbon left? e. Use a complete sentence to explain how you found the answer to part (d). f. What mathematical operations did you perform to find the answer to part (d)? g. Write an equation that you can use to find the amount of bows Joyce will have made if she has 25 feet of ribbon left. Chapter 1 Assignments 1
Lesson 1.1 Assignment page 2 h. Solve the equation from part (g) to find the number of bows that will make the equation true. Name the inverse operations you are using in each step. 2 Chapter 1 Assignments
Lesson 1.2 Assignment Name Date Why Doesn t This Work? Equations with Infinite or No Solutions 1. The population growth (in thousands) for a small town near Bay City can be represented by the expression x 1 4 (x 1 315), where x represents the number of years since 2005. 5 The population growth (in thousands) for a neighboring town can be represented by the expression 2x 2 1 (x 2 630), where x represents the number of years since 2005. 5 a. The governor of the state would like to know when the populations of the two towns will be equal. Use the expressions above to write and solve an equation to determine the year. Chapter 1 Assignments 3
Lesson 1.2 Assignment page 2 b. Substitute the values from the table into the expressions on each side of the equation and evaluate them. Show your work. Years since 2005 x 1 4 5 (x 1 315) 2x 2 1 (x 2 630) 5 4 8 12 15 4 Chapter 1 Assignments
Lesson 1.2 Assignment page 3 Name Date c. Does it appear that the expressions are equivalent based on the values in the table? Does it appear that the populations will be equal at some point in time? d. Graph each expression on your graphing calculator and sketch the graphs. Population (thousands) 300 250 200 150 100 50 0 0 2 4 6 8 10 12 14 16 18 Years since 2005 e. What do you notice about the graphs? f. What does this mean in terms of the year that the populations will be the same? Chapter 1 Assignments 5
Lesson 1.2 Assignment page 4 2. Two neighboring towns are not having population growth. In fact, they both have been losing population since 1995. The population decline for one of the towns (in thousands) can be represented by the expression 2 2 (x 2 500), where x represents the number of years since 1995. 5 The population decline for the other town (in thousands) can be represented by the expression 2 1 x 1 1 2 (x 1 2000), where x represents the number of years since 1995. 10 a. In what year will the populations of both towns be the same? Write and solve an equation that represents this situation. b. What does your answer from part (a) suggest about the graphs of the two population declines? 6 Chapter 1 Assignments
Lesson 1.3 Assignment Name Date Who Has the Most? Solving Linear Equations The Franklin Lee Middle School Glee Club is hosting a Talent Show competition to raise money for a community that was recently hit by a flood. All the members are asked to go out in the community to sell tickets to the show. Patrick sold 30 more tickets than Jose. Gabriella sold 25 less than two times the amount Patrick sold. Owen sold a third of the amount of tickets than Patrick sold. Desmond sold 15 less than Owen. 1. Define a variable for the number of tickets Jose sold. a. Write algebraic expressions for the number of tickets that each student sold in terms of the number of tickets Jose sold. The number of tickets Patrick sold: The number of tickets Gabriella sold: The number of tickets Owen sold: The number of tickets Desmond sold: b. If Jose sold 30 tickets, how many tickets did each of the others sell? The number of tickets Patrick sold: The number of tickets Gabriella sold: The number of tickets Owen sold: The number of tickets Desmond sold: Chapter 1 Assignments 7
Lesson 1.3 Assignment page 2 c. If Gabriella sold 65 tickets, how many tickets did each of the others sell? The number of tickets Jose sold: The number of tickets Patrick sold: The number of tickets Owen sold: The number of tickets Desmond sold: 8 Chapter 1 Assignments
Lesson 1.3 Assignment page 3 Name Date d. If Patrick, Owen and Desmond sold 175 tickets altogether, how many tickets did each of them sell? The number of tickets Jose sold: The number of tickets Patrick sold: The number of tickets Gabriella sold: The number of tickets Owen sold: The number of tickets Desmond sold: Chapter 1 Assignments 9
Lesson 1.3 Assignment page 4 e. Can Jose and Patrick sell the same amount of tickets as Gabriella? Explain. 10 Chapter 1 Assignments
Lesson 1.4 Assignment Name Date Games and Practice Solving More Linear Equations Javier has four different chicken coops on his farm. He gathers eggs from each coop every day to sell at the local farmer s market each week. During one week in the summer, the production levels from each coop were compared. The number of eggs from coop B can be found by subtracting 10 from coop A s production, then multiplying this result by two fifths. The number of eggs from coop C can be found by first adding 3 to coop A s production, multiplying this amount by 3, subtracting four from this total, then dividing the whole result by 4. The number of eggs from coop D can be found by adding 7 to coop A s production, doubling this amount, then dividing the result by 3. 1. Define a variable for the number of eggs produced by coop A. Then write expressions for the number of eggs produced by the other coops. The number of eggs produced by coop B: The number of eggs produced by coop C: The number of eggs produced by coop D: a. If coop A produced 125 eggs, how many did each of the other coops produce? The number of eggs produced by coop B: The number of eggs produced by coop C: The number of eggs produced by coop D: Chapter 1 Assignments 11
Lesson 1.4 Assignment page 2 b. If the sum of the number of eggs from coop B and coop C was 24 more than the number of eggs from coop D, how many eggs did each coop produce? 12 Chapter 1 Assignments
Lesson 1.4 Assignment page 3 Name Date The number of eggs coop A produced: The number of eggs coop B produced: The number of eggs coop C produced: The number of eggs coop D produced: Chapter 1 Assignments 13
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