Scenario #1: You handle internal accounting for Anderson Homes, a land/housing developer. The company purchased land in Central Arkansas and developed 200 acres. Two orders were recently placed with a nursery by the company’s landscapers. The invoices from the orders do not list the per-item price.
a) After contacting Nursery A, they inform you that the first order that was placed was for 13 Hydrangea bushes and 4 Dogwood trees at a cost of $487. Use x to represent bushes and y to represent the trees. Write an equation that illustrates the situation.
b) Nursery A later indicates that the second order called for 6 Hydrangea bushes and 2 Dogwood trees at a cost of $232. Write an equation that illustrates this situation. Write an equation that illustrates this situation using the same variables you used in part a.
c) Use the equations from part a and b as a system of equations. Use elimination to determine the cost of each. Describe the steps you used to solve the problem.
Scenario #2: The mortgage department of the company is selling two model homes that are located on the same block. The square footage, as well as the type of model, determines the cost of these homes.
e) The second home has 1000 square feet less than twice the square feet of the first home. Write an equation that illustrates this situation using x and y to denote home #1 and home #2, respectively.
f) Together, both homes have 4,400 square feet. Write an equation that illustrates this situation using the same variables you used in part e.
g) Use substitution to determine the square footage of each house. Explain how you arrived at your answer.
h) The market gives a cost per square footage at $49.70. How much will each home cost before upgrades/amenities? Explain
Scenario #3: Your company must use a transportation service to shuttle their corporate partners from the airport for a quarterly meeting. Crespo Transportation Service charges $32 initially plus $8 per mile for every mile traveled. Siera Transportation Service charges $24 initially plus $10 per mile for every mile traveled.
i) Write an equation in two variables (x & y) that illustrates the costs for the Crespo Transportation Service.
j) Write an equation in two variables (x & y) that illustrates the costs for the Siera Transportation Service.
k) If the trip is 3 miles, how much does each one charge? If the trip is 6 miles, how much does each one charge? Explain
l) At what mileage are both services charging the same rate? Explain
m) If you were to graph this system of linear equations, what is happening “graphically”, where the services are charging same rate? Explain
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