“The biggest disease in north america is busyness”
Thomas Merton
From coast to coast north american has many wonders. Home to to variety of different landscapes, vegetation, animals, culture, and most of all sports teams. As we study how linear relations have a impact on our decision making it is time to put this knowledge to use. For this unit we have been handed a project dubbed “the illest road trip”.
The goal is to use linear relations and other mathematical operations to help plan a road trip that will cost between $18000 and $17500. A tall task for anyone but using the tools provided I began to understand the true nature behind linear relationships, and planned truly the illest road trip OF ALL TIME.
Car’s, Hotels, Food, and Luggage
The first step in planning this trip is to figure out how much Hotels, food and luggage will cost. For this I had to deliberate what I wanted to trip to feel like. I had always wanted it to be a high class trip so I decided I wanted it to get the highest quality cuisine and highest quality of hotels. This would allow me to both reach the spending requirements in my trip and allow me to enjoy it without any worries of not having the funds.
The high quality cuisine costs $200 per person. It will cost a total 400 dollars per day because I am bringing along one other person on my great road trip. For hotels it will cost $500 per day. This means I am now up $900 per day for hotels and food. When choosing this I am remaining mindful of the importance of these numbers in my linear equations. This number will be my coefficient in my linear equation.
y = d(900) y = cost (dependant variable) d = days (independent variable)
The next key idea is to figure out is how much luggage will cost during the trip. I decided to use duffel bags as my luggage. This would free up some more cash for any amenities I wanted to experience on the trip. Duffel bags will cost 75 per person, so because I have 2 people on this trip it will cost 150 dollars. This tells me the fixed value in the linear equation
y = d(900) + 150
I have now completed the linear equation for half of the project. To help makes things a bit simpler for me I decided put this linear equation into a excel spreadsheet. This would prove very helpful later on the project
When choosing a car its key to understand what you want this trip to be like. When I want a trip to be high style you can’t drive around in a camry. You gotta go for it all and I choose the lambo for those very reasons. The one major drawback of choosing this car is both its high price and its terrible mileage. For the linear equation that corresponds to the car the fixed number will be the cost of gas, the numerical coefficient the cost per day to rent the car, the independent variable will days once again and the dependant variable will be cost.
The cost to rent the lambo is 160 per day. So this fills out half of the the linear equation for cars
y = d(160)
Before we can enter the cost of gas we must first choose our destinations and derive the distance. Using google maps I began to plan out my route, making sure that time driven between each of my major destination is not over 10 hours. 
This route would visit many booming metro’s and many cultural hubs. The 3 biggest destinations would be Atlanta, San Francisco, and Las Vegas. In total this would take 115 hours to drive and would traverse 7497 miles.
After factoring in the city driving and highway driving i figured out that I would need 571.3 gallons of gas. Multiply that by the corporate rate for gasoline and you get the total price for gas on the trip, $1599.64. I could now finish of the linear equation for the car side of the project
y = d(160) + 1599.64
I added this to my spreadsheet, and I am now ready to move onto the totaling up these two equations into one large linear relationship.
This large linear equation would allow me to begin graphing to total cost of the trip.
y = (d(900) + 150) + (d(160) + 1599.64) y = (d(900 + 160) + 1599.64 + 150
Creating this equation allowed me the ability to graph my data, and it was easy to figure out that a fifteen day trip would be ideal for the cost i needed it to be.
This left only one thing to do is to graph the sponsorship money I will get and choose the one that best fits my needs. I first had figure out the linear equations when I was just given both variables. 
After that it is simply a piece of cake to to graph it to figure out which one is the best for me.
With I choose the snapple option, so it kept me above the minimum spending limit for my trip. THis would be sure to be an amazing trip and I hope I could someday take part in something like this.
