Can somebody help me please? 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 rep. 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. I know this is x+y=38. But after that I get lost with the rest of this problem
b.) The rep. 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 the situation. Use the same variables you used in part a.
c.) Use elimination to determine how many house with each floor plan are available. Explain how you arrived at your answer. HELP!!!! ME!!!! PLEASE!!!!
x = number of houses with floor plan 1
y = number of houses with floor plan 2
x(175,000) + y(200,000) = 7,200,000
7,200,000 is the value of the 38 houses
made up of a number of plan 1 houses (x) and a number of plan 2 houses (y).
Then solve simultaneously to find x and y.
First tidy up the above equation
x+(200/175)*y = (7200/175)
x+(8/7)*y = (288/7)
now solve
x + y = 38 and
x + (8/7)y = (288/7)
to get y = 22 and x = 16.
Ok, hope that helps
a.) The equation that illustrates the situation is x + y = 38 because there are 38 homes available in total, denoted by x and y for floor plan #1 and floor plan #2, respectively.
b.) To create an equation for the value of all the available houses, we multiply the number of houses of floor plan #1 (x) by its price ($175,000) and add it to the number of houses of floor plan #2 (y) multiplied by its price ($200,000). This should equal the total value of all the available houses, which is $7,200,000. Therefore, the equation is: 175,000x + 200,000y = 7,200,000.
c.) To determine how many houses there are with each floor plan, we can solve the system of equations formed by equations (a) and (b) using the method of elimination.
First, we can multiply equation (a) by 175,000 to match the coefficients of x:
175,000(x + y) = 38 * 175,000
175,000x + 175,000y = 6,650,000
Now we have two equations:
175,000x + 175,000y = 6,650,000
175,000x + 200,000y = 7,200,000
Next, we subtract the first equation from the second equation to eliminate the x variable:
(175,000x + 200,000y) - (175,000x + 175,000y) = 7,200,000 - 6,650,000
200,000y - 175,000y = 550,000
Simplifying, we get:
25,000y = 550,000
Dividing both sides of the equation by 25,000:
y = 550,000 / 25,000
y = 22
Now we can substitute the value of y back into equation (a) to find x:
x + 22 = 38
x = 38 - 22
x = 16
Therefore, there are 16 houses with floor plan #1 and 22 houses with floor plan #2.