The representative tells you that floor plan #1 sells for $225,000 and floor plan #2 sells for $300,000. She also mentions that all the available houses combined are worth $10,350,000. Write an equation that illustrates this situation. Explain. Use the same variables you used in part a.
Is this right?:
255,000x+300,000y=10,350,000
yes, correct.
I have to use the elimination method to solve this system of equations but, I just do not get it.
x+y=42
255,000x+300,000y=10,350,000
Yes, your equation is correct.
To explain the equation, let's assign variables to the unknowns in the problem. We will use:
- x for the number of houses that are sold with floor plan #1
- y for the number of houses that are sold with floor plan #2
According to the given information, we know that each house sold with floor plan #1 is worth $225,000 and each house sold with floor plan #2 is worth $300,000. So, for x houses sold with floor plan #1, the total value would be 225,000x. Similarly, for y houses sold with floor plan #2, the total value would be 300,000y.
The problem also states that the combined worth of all the available houses is $10,350,000. Therefore, we can write the equation as follows:
225,000x + 300,000y = 10,350,000
This equation represents the total value of all the available houses, with the left side representing the value of the houses sold with floor plan #1 and #2, and the right side representing the total worth of all the available houses combined.