(I'm so lost with all this algebra so can someone please help me? I have tried to put some answers in so please tell me if any of my answers are wrong and help with the ones left blank).
2. 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. 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. $175,000(x)+$200,000(y)=$7,200,000
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
both your equations are correct, but let's reduce your second equation.
$175,000(x)+$200,000(y)=$7,200,000
175,000x + 200,000y = 7,200,000
divide by 1000
175x + 200y = 7200
divide by 25
7x + 8y = 288
now multiply your first equation by 7
7x + 7y = 266
subtract the two equations.
y = 22
back in the first
x + y = 38
x + 22 = 38
x = 16
re your other question, I don't see how I could improve on Quiddich's solution.
To use elimination to determine the number of houses with each floor plan, we can solve the system of equations formed in part (a) and (b) simultaneously.
Let's start by multiplying the equation obtained in part (a) by 175,000 (the value of floor plan #1) and the equation obtained in part (b) by 200,000 (the value of floor plan #2). This is done to make the coefficients of either x or y equal in both equations, allowing us to eliminate one of the variables.
Multiply the equation from part (a) by 175,000:
175,000(x + y) = 175,000(38)
175,000x + 175,000y = 6,650,000
Multiply the equation from part (b) by 200,000:
200,000($175,000x) + 200,000($200,000y) = 200,000($7,200,000)
35,000,000x + 40,000,000y = 1,440,000,000
Now, we have the following system of equations:
175,000x + 175,000y = 6,650,000
35,000,000x + 40,000,000y = 1,440,000,000
To eliminate one of the variables, we need to multiply the first equation by a suitable factor and subtract it from the second equation. In this case, multiplying the first equation by 40,000 will lead to the elimination of the variable y.
Multiply the first equation by 40,000:
40,000(175,000x + 175,000y) = 40,000(6,650,000)
7,000,000x + 7,000,000y = 266,000,000
Now, subtract this equation from the second equation:
(35,000,000x + 40,000,000y) - (7,000,000x + 7,000,000y) = 1,440,000,000 - 266,000,000
28,000,000x + 33,000,000y = 1,174,000,000
We now have a new equation:
28,000,000x + 33,000,000y = 1,174,000,000
To solve this equation, we can divide it by 1,000,000 to simplify:
28x + 33y = 1,174
Now we have a simplified system of equations:
175,000x + 175,000y = 6,650,000
28x + 33y = 1,174
Using this system, we can solve for x and y using any method of solving simultaneous equations like substitution or elimination.