I need someone to review this and see if it is correct please
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.
X+Y=56
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.
3x=y
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.
X+3x=56
Add
4x=56
Divide by4
X=14
Y=3x=3(14)=42
14 of plan 1 and 42 of plan 2
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?
X=56 and y=56 (0,56) and (56,0) both intercepts are at (0,0) the lines would intersect at x=14, y=42 which is (14,42)
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.
X+y=38
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.
175,000x+200,000y=7,200,000
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Multiply by -175,000
-175,000x-175,000y=-6,650,000
Add
25,000y=550,000
Divide by 25,000
Y=22
X+22=38
X=38-22=16
16 of plan 1 and 22 of plan 2
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?
Heavy lifting 80+35(2)=80+70=150 Quick move 55(2)=110
Quick move provides the better deal
b) Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
Heavy lifting 80+35915)=80+525=605
Quick move 55(15)=825
Heavy lifting has the better deal
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.
Quick move is less than Heavy lifting
55h<80+35h
Subtract 35h
20h<80
Divide by 20
H<4 Quick move has the better deal.
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.
X+Y=56
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.
3x=y
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.
X+3x=56
Add
4x=56
Divide by4
X=14
Y=3x=3(14)=42
14 of plan 1 and 42 of plan 2
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?
X=56 and y=56 (0,56) and (56,0) both intercepts are at (0,0) the lines would intersect at x=14, y=42 which is (14,42)
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.
X+y=38
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.
175,000x+200,000y=7,200,000
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Multiply by -175,000
-175,000x-175,000y=-6,650,000
Add
25,000y=550,000
Divide by 25,000
Y=22
X+22=38
X=38-22=16
16 of plan 1 and 22 of plan 2
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?
Heavy lifting 80+35(2)=80+70=150 Quick move 55(2)=110
Quick move provides the better deal
b) Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
Heavy lifting 80+35915)=80+525=605
Quick move 55(15)=825
Heavy lifting has the better deal
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.
Quick move is less than Heavy lifting
55h<80+35h
Subtract 35h
20h<80
Divide by 20
H<4 Quick move has the better deal.
You need to type out the information rather than copy and paste.
1. a) The equation that illustrates the situation is X + Y = 56, where X represents floor plan #1 and Y represents floor plan #2. This equation represents that the total number of houses available, represented by X and Y, is equal to 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 3X = Y. This equation represents that Y, the number of houses with floor plan #2, is equal to 3 times X, the number of houses with floor plan #1.
c) To determine how many of each type of floor plan is available, we can use substitution. We can substitute the value of Y from equation b) into equation a). So, we have X + 3X = 56. Simplifying this equation, we get 4X = 56. Dividing both sides by 4, we find that X = 14. To find Y, we substitute the value of X back into equation b), giving us Y = 3X = 3(14) = 42. Therefore, there are 14 houses available with floor plan #1 and 42 houses available with floor plan #2.
d) The intercepts of the equation from part a) are X = 56 and Y = 56, which means the points (0, 56) and (56, 0). The intercepts of the equation from part b) are X = 0 and Y = 0, which means the point (0, 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 where there are two floor plans available and 38 homes available is X + Y = 38, where X represents floor plan #1 and Y represents floor plan #2.
b) The equation that illustrates the situation where floor plan #1 sells for $175,000, floor plan #2 sells for $200,000, and the total value of all the available houses is $7,200,000 is 175,000X + 200,000Y = 7,200,000, where X represents the number of houses with floor plan #1 and Y represents the number of houses with floor plan #2.
c) To determine how many houses with each floor plan are available, we can use elimination. Multiply the equation from part a) by -175,000, we get -175,000X - 175,000Y = -6,650,000. Adding this equation to the equation from part b), we get -175,000X - 175,000Y + 175,000X + 200,000Y = -6,650,000 + 7,200,000. Simplifying, we have 25,000Y = 550,000. Dividing both sides by 25,000, we find that Y = 22. Substituting this value for Y back into the equation from part a), we have X + 22 = 38. Simplifying, we get X = 16. Therefore, there are 16 houses available with floor plan #1 and 22 houses available with floor plan #2.
3. a) To determine which mover provides a better deal for 2 hours of work, we can calculate the total cost for each mover. For Heavy Lifters, the total cost is $80 + $35(2) = $80 + $70 = $150. For Quick Move, the total cost is $55(2) = $110. Therefore, Quick Move provides the better deal, as it is cheaper at $110 compared to $150 for Heavy Lifters.
b) To determine which mover provides a better deal for 15 hours of work, we can calculate the total cost for each mover. For Heavy Lifters, the total cost is $80 + $35(15) = $80 + $525 = $605. For Quick Move, the total cost is $55(15) = $825. Therefore, Heavy Lifters provides the better deal, as it is cheaper at $605 compared to $825 for Quick Move.
c) To find the range of hours where Quick Move offers the better deal, we can set up an inequality. The cost for Quick Move, represented as 55h, should be less than the cost for Heavy Lifters, represented as 80 + 35h. So the inequality is 55h < 80 + 35h. By subtracting 35h from both sides, we get 20h < 80. Finally, dividing both sides by 20, we find h < 4. Therefore, Quick Move provides the better deal for values of h less than 4 hours.