# The Cycle Shop Performance Task

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1 The Cycle Shop Performance Task Did you enjoy this activity? Why or why not? How do you think this type of activity compares to more traditional math practice problems? Do you think this type of activity helps you understand systems more? Do you think it will help you prepare for your test? Mathematical Accuracy Completing all computation and algebraic manipulation correctly Mathematical Precision Showing appropriate work in an organized and clear manner Reflection + Writing Answered all writing portions of the activity in a thoughtful and complete way Name: Section: 12

2 The Cycle Shop Part A C.. Describe your solution method and explain your final answer: For this task you will pretend that you work for a small business that rents bicycles (b), tricycles (t), and tandem bikes (z). The cycles are often coming and going in and out of the shop, so there is always a different number of bikes in the shop. A. Fill in the following table with the information about the different types of cycles: Bicycle Tricycle Tandem Number of Wheels Number of Seats Number of Pedals D. If each cycle in the shop was rented for 1 hour the shop would make \$1799. Use the rental prices from part D and your solutions to check your work: B. Write 3 equations using the variables b, t, and z, with each one representing the number of wheels (w) for each type of cycle: w = b w = t w = z 2 11

3 The Cycle Shop Part E It is a month later and a worker takes inventory of all cycles in the Cycle Shop and observes three things: 1) there are a total of 144 cycles 2) there are a total of 378 pedals 3) there are a total of 320 wheels A. Write 3 equations, using b, t, z, representing the three things the worker noticed. Equation 1: Equation 2: Equation 3: C. Write a single algebraic equation that represents the total number of wheels for all cycles (W) in the shop. W = + + D. On Monday you counted 48 tricycle wheels. How many tricycles were in the shop that day? E.. On Tuesday you counted 96 wheels in total. Come up with THREE different possible combinations of bicycles, tricycles and tandem bikes. B. Figure out how many bicycles, tricycles, and tandem bikes are in the shop on that day using the solving systems methods we have discussed in class. F. On Tuesday you also counted 122 pedals at the store. Come up with THREE different possible combinations of bicycles, tricycles and tandem bikes. G. Use the guess and check method to determine what combination of bicycles, tricycles and tandem bikes would result in 96 wheels and 122 pedals: 10 3

4 The Cycle Shop Part B C. What is the best option for Steve and Kylie so they can ride together for the longest amount of time? On Wednesday there were no tandem bikes in the shop. There were only bicycles and tricycles. There are a total of 24 seats and 61 wheels in the shop. A: Write two equations that represent this information: Equation 1: Equation 2: B. Solve your system of two equations using any method you choose. Show all work. D. Steve and Kylie decide to invite their friend Ray to come with them. Together, now they have \$100. Determine the longest number of hours they can ride together and what combination of cycles they should rent. Number of tricycles: Number of bicycles: C. Check your solutions by plugging your answers back into BOTH equations to confirm you are correct: D. Which method did you choose to solve your system: 4 9

5 The Cycle Shop Part D Below is the cost information for bike rentals at your shop: Bicycles rent for \$12/hour. Tricycles rent for \$10/hour. Tandem bikes rent for \$15/hour. On Thursday there were still no tandem bikes in the shop. There were only Bikes and trikes. There was a total of 16 cycles in the shop and the number of bicycles was three times the number of tricycles. A: Write two equations that represent this information: Equation 1: Equation 2: B. Solve your system of two equations using any method you choose. Show all work. Rentals are only available for whole hours. A. Steve has \$32. What is the maximum # of hours he could rent each cycle? B. Steve and Kylie together have \$73 and want to ride together for as long as their money will allow. Fill in the following table: Number of tricycles: Number of bicycles: 1 hr 2 bicycles 2 tricycles 1 bike/1 trike 1 tandem C. Check your solutions by plugging your answers back into BOTH equations to confirm you are correct: 2hrs 3hrs 4hrs 5hrs D. Which method did you choose to solve your system: Explain why you chose that method: 8 5

6 The Cycle Shop Part C A. On Thursday you inventory all the cycles in the shop and you notice 2 things: The total number of cycles in the shop is 32 and the total number of wheels in the shop is 86. Write an equation for each of these observations: D. On Friday at inventory you notice 3 things: There were a total of 47 bikes in the shop, the number of bicycles was 3 more than the tricycles and the number of tandem bikes was seven less than the number of tricycles. Write THREE equations for these observations: Equation 1: Equations 2: Equation 3: Equation 1: Equation 2: E. Use substitution to solve your system (HINT: Substitute equation 2+3 into equation 1 at the same time to get a one variable equation!) B. How can we eliminate two variables from this system of equations in at the same time? C. Using that insight, figure out how many bicycles, tricycles, and tandem bikes are in the shop that day: Bicycles: Tricycles: Tandem Bicycles: Plug your answer into both your equations to check if you are correct: Bicycles: Tricycles: Tandem Bicycles: Plug your answer into all three of your equations to check if you are correct: 6 7

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