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 40 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 $168,000 and floor plan two sells for $212,000. She also mentions that all the available houses combined are worth $7,380,000. 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.
a. Let's use the variables x and y to represent the number of floor plan one and floor plan two homes respectively. Since there are only 40 homes still for sale, the equation can be written as:
x + y = 40
b. We know that floor plan one sells for $168,000 and floor plan two sells for $212,000. If we multiply the number of houses of each floor plan by their respective prices and add them together, the total value of all available houses is $7,380,000. So the equation can be written as:
168,000x + 212,000y = 7,380,000
c. To determine the number of houses available in each floor plan using elimination, we need to eliminate one variable by adding or subtracting the equations.
We have the equations from parts a and b:
x + y = 40
168,000x + 212,000y = 7,380,000
To eliminate one variable, we can multiply the first equation by a suitable number that makes the coefficients of either x or y the same. In this case, we can multiply the first equation by 168,000 to make the coefficients of x match:
168,000(x + y) = 168,000(40)
168,000x + 168,000y = 6,720,000
Now, we have two equations:
168,000x + 168,000y = 6,720,000
168,000x + 212,000y = 7,380,000
By subtracting the first equation from the second equation, we can eliminate x:
(168,000x + 212,000y) - (168,000x + 168,000y) = 7,380,000 - 6,720,000
Simplifying, we get:
44,000y = 660,000
Now, we can solve for y by dividing both sides of the equation by 44,000:
y = 660,000 / 44,000 = 15
So there are 15 floor plan two houses available. To find the number of floor plan one houses, we can substitute this value of y back into the first equation:
x + 15 = 40
x = 40 - 15
x = 25
Therefore, there are 25 floor plan one houses available.
Using elimination, we determined that there are 25 houses available in floor plan one and 15 houses available in floor plan two.