Lesson 6.1 Assignment

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1 Lesson 6.1 Assignment Name Date Perfectly Proportional Proportional Situations, Part 1 A local clothing boutique, Dress Me Up, is analyzing sales patterns at different times of the year. They sell women s, men s, and children s clothing. 1. The business manager determines that four out of every seven items sold is a piece of men s clothing during the month of May. a. Write a ratio that compares the number of items sold to the number of pieces of men s clothing sold. b. Dress Me Up sells 126 items of clothing over a weekend. How many pieces of men s clothing did they sell? 2. The business manager creates a table of values representing the total number of items sold and the number of pieces of women s clothing sold during the month of April. Analyze the table. Total Number of Items Sold Number of Women s Pieces Sold Expression t a. Complete the table of values. b. Describe how you determined the expression in the last row. Chapter 6 Assignments 89

2 Lesson 6.1 Assignment page 2 c. Dress Me Up sells 544 items during a huge sale. How many pieces of women s clothing did they sell? 3. The business manager creates a graph to show the relationship between the total number of items sold and the number of pieces of children s clothing sold during the month before the first day of school. y Number of Pieces of Children s Clothing Sold Total Items Sold x a. What is the rate of change and the y-intercept of the graph? Explain what they mean in terms of the problem situation. 90 Chapter 6 Assignments

3 Lesson 6.1 Assignment page 3 Name Date b. Dress Me Up sells 85 items of clothing during a slow week. How many pieces of children s clothing did they sell that week? Chapter 6 Assignments 91

4 92 Chapter 6 Assignments

5 Lesson 6.2 Assignment Name Date Post-Secondary Proportions Proportional Situations, Part 2 Victoria collects coins from all over the world. She is reorganizing her collection into coins from Europe and coins from other parts of the world. After sorting the coins she comes to the conclusion that six out of every ten of the coins in her collection come from Europe. 1. Write each ratio. a. the number of European coins to the total number of coins b. the number of non-european coins to the total number of coins c. The number of European coins to the number of non-european coins 2. Victoria has 230 coins in her collection. Determine the number of European and non-european coins she has in her collection. Show your work. 3. Victoria adds to her collection while keeping the same ratio of coins and now has 180 European coins. Determine the number of non-european coins and the total number of coins in her collection. Show your work. Chapter 6 Assignments 93

6 Lesson 6.2 Assignment page 2 4. Write an equation to determine the number of European coins E if Victoria has t total coins. Show your work and identify the constant of proportionality. 5. Write an equation to determine the number of non-european coins N if Victoria has t total coins. Show your work and identify the constant of proportionality. 6. Graph your equations from Questions 4 and 5 on the coordinate plane provided. Label the axes and each graph. y x 94 Chapter 6 Assignments

7 Lesson 6.3 Assignment Name Date Proportional Pay Proportional vs. Non-Proportional Relationships A new shopping center is opening this month. Before agreeing to open shops in this shopping center, store managers had to consider the monthly rent and whether they wanted to pay a one-time fee to put their shop name on the sign in front of the shopping center. Two shops, Kiki s Kupcakes and the Sewing Circle agree to open their shops in this new shopping center. Their rent payments are shown. Kiki s Kupcakes Number of Months Total Rent Paid 2 $ $16,750 8 $23, $28, $33,200 Sewing Circle Number of Months Total Rent Paid 3 $ $10,000 6 $15,000 9 $22, $27, Analyze the rent payments of each shop. a. Determine the monthly rent for each shop. Show your work. b. Did either shop pay the one-time fee to have their shop name on the sign? Explain your reasoning. Chapter 6 Assignments 95

8 Lesson 6.3 Assignment page 2 2. Consider the rent relationships presented in Question 1. a. Write an equation to represent each rent relationship. b. Label the graph that represents the rent relationship of Kiki s Kupcakes as y 1 and the rent relationship of the Sewing Circle as y 2. y Total Rent Paid Months x 3. Identify each rent relationship as proportional or non-proportional. Explain your reasoning. 96 Chapter 6 Assignments

9 Lesson 6.4 Assignment Name Date Doing Math In a Proportional Way Proportional Applications Daisa attends college in another state. She drives 540 miles on the highway to get to school. During summer break and winter break she drives home from college to visit her family and friends. 1. Daisa decides to keep track of the time it takes her to drive the 540 highway miles from school. She records her distance after a certain number of hours. She does this for both her drive home for winter break and summer break. Her data are shown. Winter Break Time (hours) Distance (miles) Summer Break Time (hours) Distance (miles) a. Which trip represents a proportional relationship? Explain your reasoning. b. Why might one trip be proportional while the other is non-proportional? Chapter 6 Assignments 97

10 Lesson 6.4 Assignment page 2 2. One of Daisa s high school classmates, Tymar, attends college with Daisa. He also drives home during the breaks. However, he takes the long way which results in 600 miles of highway driving. He records his distance after a certain number of hours for summer break. His data are shown. Summer Break Time (hours) Distance (miles) a. Daisa s driving times for summer break are shown on the graph. Graph Tymar s driving times for summer break. y Daisa Distance (miles) Time (hours) x b. Are Tymar s driving times proportional? Are Tymar s driving times proportional to Daisa s driving times? Explain your reasoning. 98 Chapter 6 Assignments

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