Student Name: Fashion Show. Your Assignment: Grade 11 Math Fashion Show Performance Task

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1 Fashion Show Your Assignment: The junior class has decided to have a fashion show in order to raise money for a class field trip. Your job is to act as a project manager and help the students design the stage and plan the show. Then you will determine the desired profit and use data to evaluate the reasonableness of doubling the actual profits. Copyright 2016 Key Data Systems 1

2 Part A: 1. The stage is equipped with curtains that hide the sets. The image shows the layout of the stage from above. Curtain 1 is 20 feet high from top to bottom. What is the minimum area of Curtain 1? A. 18 square feet B. 30 square feet C. 216 square feet D. 600 square feet 2. The students designing the outfits plan to make unisex outfits that stretch to fit students who are within 2 inches of the mean hip measurement. Assume that the hip measurements for teenage boys and girls in the 11 th grade resembles a normal distribution. If the mean hip measurement is 34 inches with a standard deviation of 2 inches, what percent of the students will be able to try out to model the clothes? A. 34 B. 36 C. 68 D. 95 Copyright 2016 Key Data Systems 2

3 Part B: 3. The costume jewelry and accessories for the show are bought from sales racks at two different stores on different days. Use x to represent the price of each item on the sales rack at the first store and y to represent the price of each item on the sales rack at the second store. On the first day, the students spent $30 on 4 items from the first store and 7 items from the second store. On the second day, the students spent $22 on 3 items from the first store and 5 items from the second store. On the third day, the students need to buy 10 items from the first store and 17 items from the second store. The class treasurer believes that he can figure out the amount of money that the students need on the third day without actually knowing the price of each item. Justify the treasurer's claim. Then check your answer by creating and solving a system of linear equations based on the first day and the second day to confirm the amount of money that the students need to purchase the items on the third day. Explain your reasoning. Copyright 2016 Key Data Systems 3

4 4. Two of the juniors volunteered to drive to the stores, but they wanted to be reimbursed for the time they spend driving to the stores and the number of miles traveled in their cars. The drivers did not charge for the cost of driving back to the school. The two drivers planned to charge a different amount for the time spent and the distance traveled because they drove different sized vehicles. The students wrote linear equations to account for the cost of driving based on the time it took to drive to the stores, x, and the number of miles traveled, y. Student A charged $2.25x + $2.00y, and Student B charged $2.75x + $1.50y. Student A determined that she will charge $ Student B determined that he will charge $ The treasurer needs to find the time and distance traveled for record keeping. He believes that it took the students 3 minutes of travel time. Determine the actual travel time, in minutes, and the number of miles traveled for each driver. Then identify the flaw in the treasurer's assumption. Explain your reasoning. Copyright 2016 Key Data Systems 4

5 5. The juniors sold the student tickets for $3 and the adult tickets for $8. Use s to represent the number of student tickets that were sold and a to represent the number of adult tickets that were sold. In total, 300 tickets were sold. After paying back the investors, the profit was $775. If the juniors initially received a total of $210 from investors, how many tickets of each type did the students sell? Explain how you calculated the values. Copyright 2016 Key Data Systems 5

6 6. Use the information from the last question to complete the following task. Is it mathematically possible to double the profits while still selling only 300 tickets? Write a model that can be used to determine the answer, and then use the actual sales to make an argument about the feasibility of doubling the profits while keeping the ticket prices the same for the second show. Are the required number of ticket sales reasonable given the data from the first show? END OF PERFORMANCE TASK Copyright 2016 Key Data Systems 6