Section 3 assessment 2

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University of Wisconsin, Milwaukee *

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102X

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Mathematics

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Apr 3, 2024

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How much coffee would you need to drink to justify the purchase of a coffee maker? Module M Culminating Activity: Part 3 Quantway® Version 2.7 © 2019 WestEd Modeling Module (Module M) Culminating Activity: The Benefits of Making Coffee at Home Citizenship, Personal Finance PROBLEM SITUATION: ESTIMATING THE COST OF COFFEE Suppose you are an avid coffee drinker who always buys a cup of coffee on your way to class. You have been considering purchasing a coffee maker for some time now. You would like to make a good financial decision based on how much coffee you drink and the relative price of buying coffee at a coffee shop versus making coffee at home. How much coffee would you need to drink to justify the purchase? In other words, when is it worth it? Part 3: Comparison (1) Fill in all the information from Part 2 below. Remember, these should be equations. Linear model for the total cost for 𝑐𝑐 cups of coffee at the coffee shop: Linear model for total cost for cc cups of coffee at home (should include coffee maker and coffee): ( Hint : Remember this may require more than one equation.) Calculating the ideal amount of coffee to justify purchasing a coffee maker involves considering the cost of the machine, the cost of beans, and the price of a cup of coffee from a café. For simplicity, let's assume the coffee maker costs $19.99, a cup's worth of beans is $0.07, and a cup of coffee from a café is $0.82. The cost per cup of coffee from home is the price of the coffee maker divided by the number of cups it makes plus the cost of the beans. If you consume one cup per day, the cost per cup is $20.07. However, the cost per cup decreases as Name: Donald Bee

Module M Culminating Activity: Part 3 Quantway® Version 2.7 © 2019 WestEd you make more coffee. If you make two cups, the cost per cup is $10.14. To determine the number of cups you need to make at home to make buying a coffee maker worthwhile, you must figure out when the cost per cup of coffee at home is lower than that of a cup from a café. Using the cost of a coffee from a café as the cost per cup of coffee at home, the equation becomes ($19.99/7) + $0.49 = $3.35. Solving for x gives us approximately 7 cups of coffee. So, if you drink more than 7 cups of coffee, purchasing a coffee maker would be a wise investment. (2) Use the equations above or the tables from Part 2 to graph each model. Be sure to include scales and labels on the axes. Let the horizontal axis be the number of cups of coffee purchased, and the vertical axis be the total amount of money each cost. Also, include a meaningful title for the graph. Make sure to label the two different models. (3) Using your graph , ESTIMATE how many cups of coffee you would need to drink at your coffee shop to justify the purchase of a coffee machine. Remember that you cannot purchase a fraction of a cup of coffee, nor can you purchase individual cups of coffee at home (coffee comes in packages). Explain how you determined your answer using your graph . (4) Use the models from Question 1 to algebraically find how many cups of coffee you would need to drink to justify the purchase of a coffee machine. (Hint: Use your algebraic models to write one equation, using only the variable c, which represents this situation.) How does this answer compare to your answer in Question 3? Remember that you cannot purchase a fraction of a cup of coffee, nor can you purchase individual cups of coffee at home (coffee comes in packages). Show your work. (5) Explain at least two limitations of the linear models.

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