Question

System of Linear 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 analyzing a real life situations using systems of linear equations to make an informed decision. The situation 1. Spending nights at a 3 star hotel in Paris, France or spending nights at a 5 star hotel in Atlanta, GAVacation 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 airplane ticket as well as the cost of the hotel per night. As an alternative, you want to look into spending the same number of nights in Atlanta 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 Atlanta that will cost you only for the hotel. Note: You are spending the same number of nights at each destination. Project Details For this project, you will need to: 1) Collect data. 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. Write a system of equations to represent the information you collected: 1st Equation: Cost of flight + hotel in Paris 2nd Equation: Hotel in Atlanta Use the methods we have been studying (graphing and solving algebraically) to determine which plan is better based on the number of nights you decide to stay.

Answer 1

To decide on a vacation to Paris or stay in Atlanta, set up two equations, one for each scenario including relevant expenses, and use graphing or algebraic solutions to compare costs effectively.

Step-by-step explanation:

When analyzing real life situations using systems of linear equations to make informed decisions, it’s essential to represent the varying costs with equations. In this case, determining whether to go on vacation to Paris, France, or stay in a 5-star hotel in Atlanta, GA involves two equations.

First, collect the data necessary for the costs of flights and hotels. The first equation would account for the cost of the flight to Paris plus the hotel cost per night, which could be represented as CP = f + hPn, where CP is the total cost of the Paris vacation, f is the flight cost, hP is the cost of the hotel per night, and n is the number of nights.

For staying in Atlanta, you only need to consider the hotel cost. The second equation would be CA = hAn, where CA is the total cost of the Atlanta stay, and hA is the cost of the hotel per night in Atlanta.

Using graphing or algebraic methods learned in class, compare these two equations to determine which option is more economical based on the number of nights you wish to stay.