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

a. X = floor plan 1

Y = floor plan 2.
X + Y + 38

b. 175,000X + 200,000Y = 7,200,000
c. Solve the two equations by elimination.
Post your work if you get stuck.

a. To write an equation that illustrates the situation, let's consider that there are x number of floor plan one homes available and y number of floor plan two homes available. According to the information provided, the sales representative mentions that there are 38 homes still for sale. This can be written as:

x + y = 38

b. Now, let's consider the prices of the floor plans. The representative states that floor plan one sells for $175,000 and floor plan two sells for $200,000. The total value of all the available homes is mentioned to be $7,200,000. Using this information, we can write the second equation as:

175,000x + 200,000y = 7,200,000

c. To determine the number of houses available in each floor plan using elimination, we can solve the equations simultaneously. First, we will multiply the first equation by 175,000 and the second equation by 200,000 to eliminate x, the number of floor plan one homes:

(175,000)(x + y) = (175,000)(38)
175,000x + 175,000y = 6,650,000

(200,000x + 200,000y) = (200,000)(38)
200,000x + 200,000y = 7,600,000

Next, we will subtract the first equation from the second equation to eliminate y:

(200,000x + 200,000y) - (175,000x + 175,000y) = 7,600,000 - 6,650,000
25,000x + 25,000y = 950,000

Now we have a new equation:

25,000x + 25,000y = 950,000

To solve for x and y, we can divide both sides of the equation by 25,000:

(x + y) = 950,000 / 25,000
x + y = 38

We can see that this new equation is the same as the first equation. This implies that the system is dependent, and we cannot determine the specific values for x and y. However, we can still conclude that there are 38 houses available in total, but we do not have enough information to determine how many houses are available in each floor plan individually.