buying a house
supposed you are in the market for a new home and are intersted in a new housong community under construction in different city.
the sales representative informs you that there are two floor plans available, and that there are a total of 56 available. use x to represent floor plan #1 and y to represent floor plan #2. write an equation.
the sales representative later indicates that there are 3 times as many houses availablr with the second floor bplan than the first . write an equation that illustrates this situation. use the same variables yyou used in part a.
use the equations from part a and b of this exercise as a system of equations. use substition to determine how many of each type of floor plan is available. describe the steps you used to solve the problem.
what are the intercepts of the equation from part of this proble? what are the intercepts from part b this problem? where would the lines intersect if you solved the system by graphing?
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.
the sales representative here tells you they also have two floor plans available but they only have 38 homes available write an equation tha illustrates this situation. use x and y to denote floor plan #1 and floor plan #2 respectively.
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 available hoses combined are worth $7,200,000. write an equation that illustrates this situation. use the same variables you used in part a.
use elimination to determine how many houses with each floor plan are available.explain how you arrived at your answer.
you recently started 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 you are unsure which company to choose. you search online and are interested in contacting two companys heavy lifters and quick move to discuss their rates. heavy lifting charges $80 fee plus $35 per hour. quick move charges $55 per hour with no additional fees.
which mover provides a better eal for 2 hours of work? how did you arrive at your answer.
whice mover provides a better deal for 15 hours of work? how did you arrive at your answer?
for what valuse h(hours) does quick move offer the better deal? epress your answer inequality. explain how you reached you answer.
please help with this i need to bring my grade up and i only have two weeks left of class and i m not good at this kind of math thank you.
You first have to do as much of this problem as you can. We'll be able to help you after we see what you understand and what you don't understand.
Start with:
The sales representative informs you that there are two floor plans available, and that there are a total of 56 available. use x to represent floor plan #1 and y to represent floor plan #2. Write an equation.
Ms. Sue has the right idea! I was trying to explain this in a big long answer, but wasn't getting anywhere useful.
Actually, I think this question is phrased confusingly. I think it should say "use x to represent _the number of houses with_ floor plan #1 and y to represent _the number of houses with_ floor plan #2. Write an equation." if that helps any.
Sure, I'll help you step-by-step with each problem.
a) To represent the number of houses for each floor plan, let x represent floor plan #1 and y represent floor plan #2. Since there are a total of 56 available houses, the equation is:
x + y = 56
b) The sales representative mentioned there are 3 times as many houses 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 part a and b using substitution, we can substitute the value of y from equation b into equation a:
x + (3x) = 56
4x = 56
x = 14
Substituting the value of x back into equation b:
y = 3 * 14
y = 42
So, there are 14 houses available with floor plan #1 and 42 houses available with floor plan #2.
d) To find the intercepts of the equations, we set each equation to zero and solve for the other variable.
For equation a: x + y = 56, let y = 0, then x = 56. The x-intercept is (56, 0).
For equation b: y = 3x, let x = 0, then y = 0. The y-intercept is (0, 0).
If you solve the system of equations by graphing, the lines would intersect at the coordinates (14, 42).
e) For the new community with only 38 available houses, the equation is:
x + y = 38
f) The sales representative mentioned that floor plan #1 sells for $175,000 and floor plan #2 sells for $200,000, with a total worth of $7,200,000. This can be represented by the equation:
175,000x + 200,000y = 7,200,000
g) To solve the system of equations from part e and f using elimination, we can multiply equation e by (-175,000) and equation f by 38:
-175,000x - 175,000y = -6,650,000
38(175,000x + 200,000y) = 38 * 7,200,000
-6,650,000 + 200,000y = 273,600,000
Combining the equations:
200,000y + 273,600,000 = -6,650,000
200,000y = -280,250,000
y ≈ -1401.25
Since the number of houses cannot be negative, we can conclude that no houses are available in this scenario.
h) To compare the rates of the two moving companies:
- For Heavy Lifters: $80 fee plus $35 per hour.
- For Quick Move: $55 per hour with no additional fees.
For 2 hours of work:
- Heavy Lifters: $80 + (2 * $35) = $150.
- Quick Move: 2 * $55 = $110.
Therefore, Quick Move provides a better deal for 2 hours of work, as it costs $110 compared to $150 for Heavy Lifters.
For 15 hours of work:
- Heavy Lifters: $80 + (15 * $35) = $605.
- Quick Move: 15 * $55 = $825.
Therefore, Heavy Lifters provides a better deal for 15 hours of work, as it costs $605 compared to $825 for Quick Move.
For values of h (hours) where Quick Move offers a better deal, we can set up the inequality:
55h < 80 + 35h
Simplifying:
20h < 80
h < 4
Therefore, for less than 4 hours of work, Quick Move offers the better deal.