A New Bakery. Your Assignment: Grade 8 Math A New Bakery

Transcription

1 A New Bakery Your Assignment: Monica and Lauren are two friends who have decided to open a bakery together. Use your knowledge of rational numbers, functions, the Pythagorean Theorem, and the volume of cylinders to help the friends set up the equipment they will need. Copyright 2016 Key Data Systems 1

2 Part A: 1. Monica and Lauren know that they will need a lot of money in order to make the purchases necessary for a successful bakery. They decide to save money each week, and once each person has contributed an equal amount to the bakery's checking account, they will have enough to move forward with their business. Monica does not initially put any money into the account but plans to deposit $ per week. Lauren decides to put an initial amount of $ into the account plus deposit an additional $ per week. Develop a model to determine the number of weeks it will take for the girls to have deposited an equal amount of money. Based on that model, enter the total amount of money in the joined account after the correct number of weeks. $ 2. One of the major costs associated with setting up a new bakery is the cost of the oven. Monica and Lauren have researched many types of ovens, and they have narrowed their search down to two brands. Both of these brands charge an initial set-up fee, plus a monthly rental fee. The total fees of each brand can be found in the table below. Brand 12-month Rental ($) 24-month Rental ($) A B The girls want to spend the least amount of money upfront for the initial set-up fee. Using that criteria, determine which brand the girls should choose, and then answer the following question. What is the monthly rental fee the girls will pay using the brand you chose? $ Copyright 2016 Key Data Systems 2

3 Part B: 3. When it is time to set up the layout of the bakery's kitchen, Monica and Lauren draw the kitchen in a coordinate plane, with each square representing one square foot. They initially decide to place a work table, Rectangle ABCD, at the locations listed in this table: Vertex Coordinate A (2, 2) B (-1, 2) C (-1, -3) D (2, -3) After the work table is placed in the kitchen, however, the girls decide it needs to be moved. The table below describes the new coordinates of the table: Vertex Coordinate A (-2, 0) B (-2, -3) C (3, -3) D (3, 0) Describe one possible transformation the girls performed on the table in order for it to be in its new location. Copyright 2016 Key Data Systems 3

4 4. In order to operate most efficiently, Monica and Lauren know that their work table needs to be close to their oven, which is represented on the girls' coordinate plane by Parallelogram EFGH. Other guidelines about the location of their oven are listed below: Point F is located at (6, 7). The distance between Point B and Point H must be 8.6 feet. The distance between Point D and Point G must be 5 feet. The area of the oven is less than 10 ft². Using the new coordinates of the work table from Question 3 and the oven guidelines, the girls determine that Point G should be located at (6, 3). Determine whether the girls are correct. If they are correct, describe the locations of the other two coordinates of the oven. If the girls are not correct, describe the mistake they made, as well as the locations of the three unknown coordinates of the oven. Copyright 2016 Key Data Systems 4

5 5. Monica and Lauren plan to buy some of their dry ingredients (particularly flour, sugar, and baking soda) in prepackaged containers. Each container with the three dry ingredients weighs 22 pounds. The weight of the sugar in each container is 2 times the amount of baking soda. Also, there are 14 pounds more flour than baking soda in each container. The girls want to calculate the weight of baking soda in each container, but they claim that the necessary equation is impossible because it has infinitely many solutions. Identify an equation that proves the girls' claim is wrong and explain why that equation does not have infinitely many solutions. Copyright 2016 Key Data Systems 5

6 6. Use these conversions to help you with Question 6: 1 pound = 16 ounces 1 foot³ of flour = ounces Monica and Lauren are almost ready to open their bakery, but first they need to buy some large cylinders for holding their dry ingredients. They decide to shop for the cylinder to hold flour first, and they find three possible choices shown below. Cylinder A has a total cost of $153.21, a diameter of 3 feet, and a height of 3.25 feet. Cylinder B has a total cost of $366.94, a diameter of 5.5 feet, and a height of 1.95 feet. Cylinder C has a total cost of $193.36, a diameter of 3.5 feet, and a height of 2.5 feet. The girls decide that they need to be able to hold 61 containers' worth of flour in one cylinder. (Use the weight of flour per container you found in Question 5 in your calculation.) Which cylinder will follow that specification and also cost the least per cubic foot? Justify your answer by using the volumes and prices of all three cylinder options. END OF PERFORMANCE TASK Copyright 2016 Key Data Systems 6