1. Imagine you are in the market for a new home and are interested in a new hous

Question

1. Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city.
a. The sales representative informs you that there are 56 houses for sale with two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.

b. The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part a.

c. Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.

d. What are the intercepts of the equation from Part a. of this problem? What are the intercepts from Part b. of this problem? Where would the lines intersect if you solved the system by graphing?

2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.

a. The sales representative here tells you they also have two floor plans available, but they only have 38 homes still for sale. Write an equation that illustrates the situation. Use x and y to denote floor plan one and floor plan two respectively.

b. The representative tells you that floor plan one sells for $175,000 and floor plan two sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in Part a.

c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.

Explanation / Answer

c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer. Substitute (38-x) for y, find x 175000x + 200000(38-x) = 7200000 175000x + 7600000 - 200000x = 7200000 175000x - 200000x = 7200000 - 7600000 25000x = 400000 x = 16 houses that cost 175,000 then 38 - 16 = 22 houses that cost 200000

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