Is this correct so far...I just want to know if I am doing this..
b) The representative tells you that floor plan #1 sells for $300,000 and floor plan #2 sells for $200,000. She also mentions that all the available houses combined are worth $3,300,000. Write an equation that illustrates this situation. Use the same variables you used in part a. (3 pts.)
300,000 + 200,000 =3300000
Multiply the first equation by 300,000
-300000x –300000 y = -5000000
Add to the second equation:
20000y = 500000
Divide by 20000:
y = 10
x +10 =
x =
of plan 1
of plan 2
To determine the values of x (representing the number of floor plan #1 houses) and y (representing the number of floor plan #2 houses), we need to solve the system of equations.
The equation you wrote to illustrate the situation is incorrect. The correct equation should be:
300,000x + 200,000y = 3,300,000
Now let's solve the system of equations step by step.
1. Multiply the first equation by 300,000:
-300,000x - 300,000y = -4,500,000
2. Add the modified equation to the second equation:
(-300,000x - 300,000y) + (300,000x + 200,000y) = -4,500,000 + 3,300,000
This simplifies to:
-100,000y = -1,200,000
3. Divide both sides of the equation by -100,000 to solve for y:
y = -1,200,000 / -100,000
y = 12
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x.
Let's use the equation:
300,000x + 200,000y = 3,300,000
Substituting y = 12:
300,000x + 200,000(12) = 3,300,000
Simplifying:
300,000x + 2,400,000 = 3,300,000
Next, subtract 2,400,000 from both sides:
300,000x = 3,300,000 - 2,400,000
300,000x = 900,000
Finally, divide both sides of the equation by 300,000 to solve for x:
x = 900,000 / 300,000
x = 3
So the number of floor plan #1 houses (x) is 3, and the number of floor plan #2 houses (y) is 12.