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. X + Y = 38
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.
175,000x + 200,000y = 7,2000,000
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
To use the method of elimination, we'll first need to multiply one or both of the equations so that the coefficients of one of the variables are the same. In this case, let's multiply the first equation by 175,000 and the second equation by 38:
175,000(X + Y) = 175,000(38)
175,000X + 175,000Y = 6,650,000 (equation 3)
38(175,000x + 200,000y) = 38(7,200,000)
6,650,000X + 7,600,000Y = 273,600,000 (equation 4)
Now we can subtract equation 3 from equation 4 to eliminate the X variable:
(6,650,000X + 7,600,000Y) - (175,000X + 175,000Y) = 273,600,000 - 6,650,000
6,475,000Y = 266,950,000
Dividing both sides of the equation by 6,475,000:
Y = 41
Now we can substitute the value of Y into the first equation to solve for X:
X + 41 = 38
X = 38 - 41
X = -3
Therefore, there are -3 houses with floor plan #1 and 41 houses with floor plan #2 available. However, it's not realistic to have a negative number of houses, so there is likely a mistake in the given information or equations.