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 200 square feet more than the square footage of the first home. Write an equation that illustrates this situation using x and y to denote home #1 (x) and home #2 (y), respectively.
f) Together, both homes have 5,000 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. Demonstrate the process you used to arrive at your answer
Scenario #3: Your company must use a transportation service to shuttle their corporate partners from the airport for a quarterly meeting. Green Transportation Service charges $12 initially plus $3.50 per mile for every mile traveled. Thomas Transportation Service charges $10 initially plus $4.50 per mile for every mile traveled.
h) Write an equation in two variables (x & y) that illustrates the costs for using the GreenTransportation Service.
i) Write an equation in two variables (x & y) that illustrates the costs for using Thomas Transportation Service.
j) If the trip is 4 miles, how much does each one charge? If the trip is 10 miles, how much does each one charge? Show your work.
k) At one mileage both services will be charging the same rate. Find that mileage and explain what is happening “graphically” where the services are charging that same rate?
I am just having problems figuring the equations. I know how to do the rest. Can you please help?
We do not do your work for you, but I will give you a start.
e) If x = first home and y = second,
x + 200 = y
f) x + y = 5000
g) I''l let you do the calculations.
h) Let x = total cost and y = miles.
x = 12 + 3.5y
i) Use similar process to h.
I'll leave the rest up to you. Once you do your work, we will be happy to check it.
Sorry for the duplication.
Sure, I'd be happy to help you with the equations. Let's start with the questions regarding the model homes:
e) The second home has 200 square feet more than the square footage of the first home. We can represent the square footage of the first home as x, and the square footage of the second home as y. Since the second home has 200 square feet more than the first, the equation would be: y = x + 200.
f) Together, both homes have 5,000 square feet. Using the same variables, we can write the equation: x + y = 5000.
Now let's move on to the transportation service questions:
h) Green Transportation Service charges $12 initially plus $3.50 per mile. Let x represent the number of miles traveled. The equation for their cost would be: y = 3.50x + 12.
i) Thomas Transportation Service charges $10 initially plus $4.50 per mile. Again, let x represent the number of miles traveled. The equation for their cost would be: y = 4.50x + 10.
j) To find the cost for each service for a given trip distance, you simply substitute the value of x into the respective equations and solve for y.
For a 4-mile trip:
For Green Transportation Service: y = 3.50(4) + 12 = 14 + 12 = $26
For Thomas Transportation Service: y = 4.50(4) + 10 = 18 + 10 = $28
For a 10-mile trip:
For Green Transportation Service: y = 3.50(10) + 12 = 35 + 12 = $47
For Thomas Transportation Service: y = 4.50(10) + 10 = 45 + 10 = $55
k) To find the mileage at which both services will charge the same rate, we need to solve the equation: 3.50x + 12 = 4.50x + 10.
-2x = -2
x = 1
Therefore, at 1 mile, both services will charge the same rate.
Graphically, it means that the cost vs. mileage graphs of both services intersect at the point (1, cost), indicating that for a trip of 1 mile, both services will charge the same amount. You can plot the cost vs. mileage graphs for both services on a graph and observe where they intersect.