1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city.
a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.
b) The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a.
c) Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.
d) What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this problem? Where would the lines intersect if you solved the system by graphing?
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.
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.
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer
Variations of this same questions have been posted repeatedly since April.
type in
sales representative
in the search line at the top right of this page and you will find all those variations and their solutions.
a) Let's represent the number of houses available for floor plan #1 as x and the number of houses available for floor plan #2 as y. Since there are a total of 56 houses available, we can write the equation:
x + y = 56
b) The sales representative mentioned that there are 3 times as many homes available with the second floor plan than the first. This can be represented by the equation:
y = 3x
c) To solve the system of equations from parts a and b, we can use the method of substitution. First, we can substitute the value of y from equation b into equation a:
x + (3x) = 56
Combining like terms, we get:
4x = 56
Dividing both sides by 4, we find:
x = 14
Now, we can substitute this value of x back into equation b to find y:
y = 3(14)
y = 42
So, there are 14 houses available for floor plan #1 and 42 houses available for floor plan #2.
d) The intercepts of the equation from part a can be found by setting x or y to 0.
- If x = 0, then y = 56 (the y-intercept)
- If y = 0, then x = 56 (the x-intercept)
The intercepts of the equation from part b can be found by setting x or y to 0.
- If x = 0, then y = 0 (the y-intercept)
- If y = 0, then x = 0 (the x-intercept)
If we solve the system of equations graphically, the lines would intersect at the point (14, 42), which represents the number of houses available for each floor plan.