Question 293158: 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.
X+y=38
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.
Found 2 solutions by richwmiller, nerdybill:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! http://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.178482.html
and also
http://www.algebra.com/algebra/homework/word/Linear_Equations_And_Systems_Word_Problems.faq.question.227832.html
Answer by nerdybill(7384)  (Show Source):
You can put this solution on YOUR website! 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.
.
Let x = number of floor plan one
and y = number of floor plan two
then
x+y=38
.
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.
.
175000x + 200000y = 7200000
.
c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.
.
x+y=38 (equation 1)
175000x + 200000y = 7200000 (equation 2)
.
Using the elimination method:
Start by eliminating y -- do this by multiplying equation 1 by -200000:
-200000x - 200000y = -7600000
175000x + 200000y = 7200000
.
ADD the two equations together:
-200000x - 200000y = -7600000
175000x + 200000y = 7200000
-----------------------------
-25000x = -400000
x = -400000/-25000
x = 16 (number of floor plan one)
.
To find number of floor plan two, use equation 1 and substitute the above into it:
x+y=38
16+y=38
y = 38-16
y =20
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