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.
3. You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.
a) Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
b) Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
c) For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer.
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Kim, if you're trying to copy and paste, it's not working. You'll need to type in your questions/problems.
Thank you for the advice. I will do that.
Ok I will get this typed out.
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 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 time 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. Asd 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.
3. You recently started the paperwork to purchase your new home, and you were just notifies that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure of which company to choose. You search online and are interested in contracting two companies, Heavy Lifters and Quick Move, to discuss there rates. Heavy Lifter charges an $80 dollar fee and $35 dollars per hour. Quick Move charges $55 dollar per hour with no additional fees.
a) Which mover provides a better deal four 2 hours of work? How did you arrive at your answer?
b) Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
c) For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer.
1. a) The equation that illustrates the situation is:
x + y = 56
b) The equation that illustrates the situation where there are 3 times as many homes available with the second floor plan than the first is:
y = 3x
c) To solve the system of equations using substitution, we can substitute the value of y from equation b) into equation a) and solve for x.
Substituting y = 3x into equation a):
x + 3x = 56
4x = 56
x = 14
Substituting the value of x back into equation a):
14 + y = 56
y = 42
Therefore, there are 14 houses with floor plan #1 and 42 houses with floor plan #2 available.
d) In part a), the intercepts of the equation x + y = 56 are:
- Intercept with x-axis (when y = 0): x = 56
- Intercept with y-axis (when x = 0): y = 56
In part b), the intercepts of the equation y = 3x are:
- Intercept with x-axis (when y = 0): x = 0
- Intercept with y-axis (when x = 0): y = 0
If we solve the system of equations by graphing, the lines would intersect at the point (14, 42).
2. a) The equation that illustrates the situation is:
x + y = 38
b) The equation that illustrates the situation that all the available houses combined are worth $7,200,000 is:
175,000x + 200,000y = 7,200,000
c) To use elimination to determine how many houses with each floor plan are available, we need to multiply equation a) by a suitable number to make the coefficients of x or y in both equations the same. In this case, we can multiply equation a) by 175,000 to match the coefficient of x in equation b).
175,000(x + y) = 175,000(38)
175,000x + 175,000y = 6,650,000
Next, we can subtract the modified equation a) from equation b) to eliminate x:
(175,000x + 200,000y) - (175,000x + 175,000y) = 7,200,000 - 6,650,000
25,000y = 550,000
y = 22
Substituting the value of y back into equation a):
x + 22 = 38
x = 16
Therefore, there are 16 houses with floor plan #1 and 22 houses with floor plan #2 available.
3. a) To find out which mover provides a better deal for 2 hours of work, we need to calculate the total cost for each mover.
For Heavy Lifters:
Total cost = $80 + ($35 × 2) = $80 + $70 = $150
For Quick Move:
Total cost = $55 × 2 = $110
In this case, Quick Move provides a better deal for 2 hours of work as they charge $110 compared to Heavy Lifters' $150.
b) To find out which mover provides a better deal for 15 hours of work, we need to calculate the total cost for each mover.
For Heavy Lifters:
Total cost = $80 + ($35 × 15) = $80 + $525 = $605
For Quick Move:
Total cost = $55 × 15 = $825
In this case, Heavy Lifters provides a better deal for 15 hours of work as they charge $605 compared to Quick Move's $825.
c) To find the values of h (hours) for which Quick Move offers the better deal, we need to determine when their total cost is lower than Heavy Lifters.
Let's set up the inequality to express this:
Quick Move's cost < Heavy Lifters' cost
$55h < $80 + $35h
$55h - $35h < $80
$20h < $80
h < 4
Therefore, for values of h (hours) less than 4, Quick Move offers the better deal.