First of all, simplify your second equation
175,000(x)+200,000(y)=7,200,000
175x + 200y = 7200
7x + 8y = 288 (#2)
multiply your first equation by 7
7x + 7y = 266 (#1)
(#2) - (#1)
y = 22
then back into original first
x + 22 = 38
x = 16
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.
175,000(x)+200,000(y)=7,200,000
c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.
Just need help with part C
175,000(x)+200,000(y)=7,200,000
175x + 200y = 7200
7x + 8y = 288 (#2)
multiply your first equation by 7
7x + 7y = 266 (#1)
(#2) - (#1)
y = 22
then back into original first
x + 22 = 38
x = 16
From part a, the equation is X + y = 38.
From part b, the equation is 175,000(x) + 200,000(y) = 7,200,000.
To use elimination, we need to eliminate one of the variables (either x or y) by multiplying one or both of the equations by suitable numbers so that the coefficients of either x or y in both equations become equal.
In this case, let's eliminate the x variable by multiplying the first equation by 175,000 and the second equation by 1:
175,000(X + y) = 38 * 175,000
175,000X + 175,000y = 6,650,000
175,000(x) + 200,000(y) = 7,200,000
The system of equations now becomes:
175,000X + 175,000y = 6,650,000
175,000(x) + 200,000(y) = 7,200,000
Subtracting the first equation from the second equation:
175,000X + 175,000y - (175,000X + 200,000y) = 6,650,000 - 7,200,000
Simplifying the equation:
-25,000y = -550,000
Dividing both sides of the equation by -25,000 to solve for y:
y = -550,000 / -25,000
y = 22
Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:
X + y = 38
X + 22 = 38
X = 38 - 22
X = 16
Therefore, there are 16 houses available for floor plan one and 22 houses available for floor plan two in the new community.