Your Assignment: Math at the Amusement Park Your math teacher has decided to sponsor a class field trip to an amusement park. Your task is to research information about the prices and other amenities that are needed to enjoy a trip to the amusement park. Copyright 2016 Key Data Systems 1
Part A: 1. A map that shows the distance from your school to the amusement park reveals that there is a right triangle formed if you draw a line from your house to the school then from the school to the amusement park, then from the amusement park to your house. The scale of the map is 1 inch for every 6 miles. What is the actual distance from your house to the amusement park? A. 13 miles B. 17 miles C. 78 miles D. 169 miles 2. The math teacher gives each student a map of the amusement park that uses a coordinate plane. The meeting location is at (0, 0) on the map. Each unit is 100 feet. The first ride that you want to try is located at the coordinates (0, 4). The next ride is located at (3, 0). If you walked in a straight line from the first ride to the second ride, how many feet would you travel? A. 300 feet B. 400 feet C. 500 feet D. 700 feet Copyright 2016 Key Data Systems 2
Part B: 3. The school has buses and vans that are available for the field trip. Each bus can transport 45 students, and each van can transport 8 students. There are 241 students going on the field trip. The school plans to use a total of 7 vehicles to transport all of the students. Your classmate sets up a system of linear equations and graphs it to determine the number of buses and vans that the school should use. Your classmate looks at the graph and claims that the lines intersect at the ordered pair (2, 5), where 2 represents the number of buses and 5 represents the number of vans. Provide reasoning to explain that your classmate's claim is incorrect. Copyright 2016 Key Data Systems 3
4. The amusement park has two plans available for the school to choose from. Plan A is listed on the table below. Cost (per vehicle) Cost (per person) $10 $30 The cost of Plan B can be calculated using the formula c = $15v + $28p, where c represents the cost, v represents the number of vehicles, and p represents the number of people. The school has a budget of $7200 for the cost of tickets and parking. If 241 students are going on the field trip, which plan should the school purchase? Explain your reasoning. Copyright 2016 Key Data Systems 4
5. Use the information from the last question to complete the following task. Assume that, including teachers, 253 people attend the field trip. The school had $10,236 available for the trip including the cost of parking and tickets. The additional teachers will not need to pay for their parking, as they received free parking vouchers from the amusement park. However, the teacher tickets will need to be paid for. Use the plan you chose in question 4 to calculate the new total price for parking and tickets. The school is going to purchase food vouchers for the people attending the field trip with the rest of their budget. If 253 people attend the field trip, write a function that can be used to calculate the amount of money, m, that voucher would be worth and evaluate the function to find the amount of money that each person will receive on their food voucher. Round to the nearest dollar and explain your steps. Copyright 2016 Key Data Systems 5
6. Use the information from the last question to complete the following task. The school is deciding whether or not teachers will be given food vouchers. If the food vouchers were only given to the students on the field trip, will the amount given to the students increase by at least $1? Use an equation to model the information then solve the equation and provide an explanation for why your answer is what it is. Round to the nearest cent if necessary. END OF PERFORMANCE TASK Copyright 2016 Key Data Systems 6