solving systems of equations vacation project

 

Name:____________________________________ Date: _________________________ Period: _____

Solving Systems of Equations Project Introduction Systems of linear equations are a useful way to solve common problems in different areas of life. One of the most powerful ways to use them is in a comparison model where two similar situations are compared side by side to determine which one is better. In this project, you will be explore a real life situation and then use systems of linear equations to decide what to buy. Spending nights at a 3-star hotel in an international city or spending nights at a 5 start hotel in a city in the United States.

Vacation  Situation: You have graduated from high school and you are planning to go on a vacation by yourself. You have always wanted to travel to an international city, but you need to consider the price of the ticket as well as the cost of hotel per night. As an alternative, you want to look into spending the same number of nights in a city in the United States at a luxurious 5-star hotel. Now you need to determine whether you should go to the international city of your choice which will cost you for flight and hotel or stay in the United States that will cost you only for the hotel. Note: You are spending the same number n umber of nights at each destination.

Assignment: Gather information from travel agencies, such as Alaska Airlines, Orbitz, Expedia, or Kayak, through their website for cost of flight and cost of hotel. Then, write a system of linear equations for the two plans and create a graph using Desmos. Use the methods we have been studying to determine which plan is better based on the number of nights you decide to stay if you had exactly $1500 to spend for this vacation.

Project Details You will decide which cities you want your vacation and staycation to be. After you decide this, you need to: 1) Collect the data if necessary. 2) Write the system of linear equations and a word problem once the data has been collected. 3) Use the methods we have been studying (graphing and solving algebraically) to find the solution to the written system. 4) Design a Multimedia Presentation for the final display of the project. That may be done on PowerPoint or Prezi. Be creative! 5) Class Presentation: Every student will do a 3-5 minute presentation of their project during class time. The project presentations will have a span of 2 class periods.

 

Name:____________________________________ Date: _________________________ Period: _____

Project Rubric  6 points = Data for the scenarios. 3 points = Data Organizer 3 points = Sources documented Must turn in a print out from travel agencies from both cities to receive full credit. 8 points = Word problem and the system of equations 2 points = All variables are defined 6 points = Both equations are accurate 8 points = Graphic solution 4 points = Each line l ine is correctly graphed on Desmos 2 points = Labels and titles 2 points = Point of intersection 8 points = Algebraic solution and explanation 4 points = Correct solving 2 points = Explain your work and how you came up with the parameters 2 points = Check 18 points = Final Project 4 points = Creativity 4 points = Contains the analysis of your equations 6 points = Final product is organized and clear 4 points = Presentation: Knowledgeable in Project 2 points = Public Speaking TOTAL 50 points

Final Project Checklist  Refer to the rubric above Make sure you have the following items on your final project… –    

Collected Data  System of linear equations with variables defined  Graphs of both equations on Desmos  Algebraic solution with work and units  Analysis: o For how many nights are the prices going to be same? If you had $1500 to spend for your vacation, which plan would you choose and why?  Multimedia Presentation 

 

Name:____________________________________ Date: _________________________ Period: _____

Vacation  Data Organizer  –    

1) Define the variables

2) Complete the following chart to help you come up with a systems of linear equations

Destination

Hotel rating

International City

United States City

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Name of hotel

Price of hotel (per night) Compare same nights

Price of flight

Linear Equation

3) Write an equation for staying in the international city of your choice.

4) Write an equation for staying in the United States City.