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 available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.
b)The representative tells you that floor plan #1 sells for $175,000 and floor plan #2 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 with each floor plan are available. Explain how you arrived at your answer.
a) To represent the number of homes available for each floor plan, we can set up the equation:
x + y = 38
Here, x represents the number of homes available for floor plan #1, y represents the number of homes available for floor plan #2, and the sum of both should be equal to the total number of homes available, which is 38.
b) To represent the value of the available homes, we can set up the equation:
175,000x + 200,000y = 7,200,000
Here, 175,000 represents the cost of each home for floor plan #1, while 200,000 represents the cost of each home for floor plan #2. The total value of all the available homes should be equal to 7,200,000.
c) To determine how many houses are available for each floor plan, we can use the method of elimination. First, let's eliminate one of the variables by multiplying both equations by suitable coefficients so that the coefficients of either x or y will cancel each other out when the equations are added.
Multiply the first equation by -175,000 to make the coefficients of x equal:
-175,000x - 175,000y = -175,000 * 38 => -175,000x - 175,000y = -6,650,000
Now, we can add this equation to the second equation:
(-175,000x + 175,000x) + (-175,000y + 200,000y) = -6,650,000 + 7,200,000
This simplifies to:
25,000y = 550,000
To isolate y, we divide both sides of the equation by 25,000:
y = 550,000 / 25,000 = 22
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 22 = 38
Subtracting 22 from both sides, we get:
x = 38 - 22 = 16
Therefore, there are 16 houses available for floor plan #1 and 22 houses available for floor plan #2.