Mat116 appendix F problem #2
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.
x = plan 1
y = plan 2
175x = plan 1 cost
200y = plan 2 cost
The two equations are, (Divided by 1000 for easier calculation)
x + y = 38
175x + 200y = 7200
Solve these equations simultaneously to find x and y.
(if you are correct, x = 16, y = 22)
To use elimination to determine how many houses are available in each floor plan, we can solve the equations from parts a and b simultaneously.
We have the equation from part a:
X + y = 38
And we have the equation from part b:
175,000X + 200,000y = 7,200,000
To eliminate one of the variables, we can multiply the first equation by 175,000 to make the coefficients of X in both equations the same:
175,000(X + y) = 175,000(38)
175,000X + 175,000y = 6,650,000
Now we can subtract the second equation from the first equation to eliminate X:
(175,000X + 175,000y) - (175,000X + 200,000y) = 6,650,000 - 7,200,000
175,000X - 175,000X + 175,000y - 200,000y = -550,000
The X terms cancel each other out, and we are left with:
-25,000y = -550,000
To solve for y, we divide both sides of the equation by -25,000:
y = (-550,000) / (-25,000)
y = 22
Now that we have the value of y, we can substitute it back into the first equation from part a to find the value of X:
X + y = 38
X + 22 = 38
X = 38 - 22
X = 16
Therefore, there are 16 houses available for floor plan one (X = 16) and 22 houses available for floor plan two (y = 22).