Systems of Linear Equations Project
Project Deadline: Tuesday, April 4, 2017@ beginning of class
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 choosing between two real life situations and then using systems of linear equations to decide what to buy. The two situations are:
1. Spending nights at a 3 star hotel in Paris, France or spending nights at a 5 star hotel in New York City.
2. Cell phone plans, comparing monthly fee and start-up costs.
3. Starting your own business
1. 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 Paris, France, 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 New York City at a luxurious 5 star hotel. Now you need to determine whether you should go to Paris which will cost you for flight and hotel or stay in NYC that will cost you only for the hotel.
Note: You are spending the same number of nights at each destination.
Assignment: Gather information from travel agencies, such as American Airline, 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. 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 $1500 to spend for this vacation.
2. Cell Phone Plans
Situation: You have graduated from high school and moved away to college. Your parents have decided that it’s time for you to pay for your own cell phone. You have to stick to a strict budget. Now you need to determine whether you should go with a plan that costs more per month but charges less up front or a plan with no up- front cost that charges more per month..
Assignment: Details for this project are at
You must choose TWO of the plans and graph both of them to compare.
3. Start a business
Situation: You have a great ide a for a new business venture. You need to apply for a grant to getstart up funds for you r company. You need to show your investors your expenses and your potential income.
Assignment: Decide what you need to start your business. Research prices of any materials you need to purchase. Determine how much you should charge for your product or service. Write a system of linear equations to determine how much you will have to sell in order to make a profit.
Project Details
You will decide which project you want to do. After you decide on a project, you will need to:
1)Collect the datanecessary.
2) Write the system of linear equations and a word problemonce the data has been collected.
3) Use the methods we have been studying (graphingandsolving by substitution or elimination) to find the solution to the written system.
4) Design the final display of the project on a poster board or powerpoint. Be creative!
Project Rubric2 points = Data for the scenarios.
(Only applicable to vacation plans)
1 points = Data
1 points = Sources documented
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 is correctly graphed
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
14 points = Final Project
4 points = Creativity
4 points = Contains the analysis of your equations
6 points = Final product is organized and clear
Final Project Checklist – Refer to the rubric above
Make sure you have the following items on your final project…
Collected Data (if necessary)
System of linear equations with variables defined
Graphs of both equations (this can be done on desmos and printed or drawn by hand)
Algebraic solution with work and units
Analysis:
- If you chose vacation plan: 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?
- If you chose Cell phone plan: At how months will both plans hare the same cost? If you had $75 to spend each month, which plan should you choose and why?
Vacation – Data Organizer
1)Define the variables
2)Complete the following chart to help you come up with a systems of linear equations
Destination / Paris, France / New York CityHotel rating / /
Name of hotel
Price of hotel (per night)
Compare same nights
Price of flight
Linear Equation
3)Write an equation for staying in Paris, France.
4)Write an equation for staying in New York, NY.
Talk and text plans – Data Organizer
1)Define the variables.
2)Express Plan A as an equation.
3)Express Plan B as an equation.
*Make sure you take into consideration that first 100 minutes of talking on the phone is free!
Business Plan - Data Organizer
1)Define the variables for your input (what materials or items you need to purchase to get started) and your Output (the product or service you will sell)
2)Complete the following chart to help you come up with a systems of linear equations
Input MaterialsProduct you will sell or service you will provide
Cost of Input materials
Price you will charge
Linear Equation
3)Write an equation for your costs.
4)Write an equation for your income from your sales.