Writing Equations from Real World Systems
When writing Systems of Equations, it is important to be able to pull out information from the story problem. When pulling out information, you will want to select variables to represent different parts of the story problem. Make sure that you are consistent when setting up these variables and you know what they represent. Once you have two or more equations set up, you are able to solve the system of equations using graphing, substitution or elimination.
Writing Equations from Real World Systems Example
Problem: Suppose you start a business assembling and selling scooters. It costs you $1500 for tools and equipment to get started, and the materials for each scooter cost $200 for each scooter. Your scooters sell for $300. (a) Write and solve a system of equations representing the total cost and revenue of your business. (b) Describe what the solution means in terms of the situation. (c) Give an example of a reasonable number of scooters you could assembly and sell in order to make a profit and find the profit you will make for that number of scooters.
(a) Write and solve a system of equations representing the total cost and revenue of your business.
Let s = scooter and let I = Income
Cost: I = 1500 + 200s
Revenue: I = 300s
The reason that I have created the Cost equation as I have - I know that I have spent at least $1500 buying tools and equipment to build the scooters. That is money that is not dependent on the scooters but I have spent no matter what. I have 200 being multiplied by s because it will cost $200 for each scooter. Therefore, if I need 4 scooters, I will plug in 4 where s is in the equation.
The reason that I have created the Revenue equation as I have - I know that I will be selling the scooters for $300 dollars. Therefore, depending on the number of scooters I sell, I will need to multiply that by the $300 to figure out my income.
Solving: (My method choice - Substitution)
Let s = scooter and let I = Income
Cost: I = 1500 + 200s
Revenue: I = 300s
The reason that I have created the Cost equation as I have - I know that I have spent at least $1500 buying tools and equipment to build the scooters. That is money that is not dependent on the scooters but I have spent no matter what. I have 200 being multiplied by s because it will cost $200 for each scooter. Therefore, if I need 4 scooters, I will plug in 4 where s is in the equation.
The reason that I have created the Revenue equation as I have - I know that I will be selling the scooters for $300 dollars. Therefore, depending on the number of scooters I sell, I will need to multiply that by the $300 to figure out my income.
Solving: (My method choice - Substitution)
(b) Describe what the solution means in terms of the situation.
The solution means that once we have made a profit of $4500/sold 15 scooters we will have broken even between cost and revenue. Therefore, any point after this will be profit
(c) Give an example of a reasonable number of scooters you could assembly and sell in order to make a profit and find the profit you will make for that number of scooters.
Scooter number: 25
Profit: $2000
The solution means that once we have made a profit of $4500/sold 15 scooters we will have broken even between cost and revenue. Therefore, any point after this will be profit
(c) Give an example of a reasonable number of scooters you could assembly and sell in order to make a profit and find the profit you will make for that number of scooters.
Scooter number: 25
Profit: $2000
Writing Equations from Real World Systems extra resources
Extra videos on how to write systems of equations based on real life examples.
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Below is an example that will allow you to practice solving systems of linear equations taking place in real world problems. The most important part for real world problems is being able to set up a successful equation. once the equation is set up, you are able to use the methods that we have learned (graphing, substitution, elimination) in order to solve for your answer.
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