Posted by Karine on .
Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city. The sales representative informs you that there are 56 houses for sale two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.

Math 116 algebra 
Tiffany,
I think it would be x+y=56

Math 116 algebra 
Karine,
thanks I thought the same. Now the second question is
The sales representative later indicates that there are three 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.
I think it would be:
x+3y=56. Is this correct? 
Math 116 algebra 
Tiffany,
I think it would be x+3x=56

Math 116 algebra 
Tiffany,
because now you have 3x=y

Math 116 algebra 
Karine,
Not quite understanding since the y is only now 3 times more than x so shouldn't the variable stay the same as in the first part when making the equation?

Math 116 algebra 
Karine,
Now using the equations from Part A and Part B. use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem

Math 116 algebra 
Tiffany,
I don't think so The second part is giving you a way to solve the problem. so if you find out whay y is then you can find out what x is.

Math 116 algebra 
Tiffany,
x+y=56
x+3x=56
56/4= 14
x=14
5614=42
y=42
check 14+42=56 or 14+(14*3)=56 
Math 116 algebra 
Tiffany,
I guess you could write it
x+y=56
4x=56
56/4=x
x=14
14+y=56
5614=y
y=52
I'm not sure how your teacher would want you to show your work. This way might be the simplest form 
Math 116 algebra 
Karine,
thank you. Now using Part A and B what is the intercepts of part A and what are the intercepts of part b? Where would the lines intersect if you solved the system by graphing?

Math 116 algebra 
Karine,
my problem with the first one is how did you get a 4 when it is 3 times as many? would that 4 be a three instead and does that change the outcome of the solution?

Math 116 algebra 
Tiffany,
well the 4 came because it says y = 3 times as many as x so for y to be 3 times as many as x there has to be 4 parts of 56 1 part is x and the remaining 3 are y. Does that help?

Math 116 algebra 
Tiffany,
I think this is right but I'm not sure on this part of your problem.
from part a, x + y = 56, then
at x = 0, y = 56. Therefore yintercept = 56
at y = 0, x = 56. Therefore xintercept = 56
from part b, y = 3x, then
This is a straight line, passing through the origin
Therefore xintercept = 0
Therefore yintercept = 0 
Math 116 algebra 
Tiffany,
Sorry this is the answer to the 2nd question.
Using the straight lines x + y = 56 and y = 3x, then they would intersect at x = 14 and y = 42 
Math 116 algebra 
Karine,
Thank you once again. I was getting the same answers but I was wondering if I was wrong. Seems you made it correct in thought for me.
Here is another one: The sales representative here tells you they also have two floor plans available at another community but on 38 homes are available. Need to write an equation using x as floor plan one and y as floor plan two.
I got x+y=38 is this one correct?
b. The representative tells you that floor plan one sells for $175,000 and floor plan two 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 the elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.
3.You recently started the paperwork to purchase your new home, and 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 Lifting 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. 
Math 116 algebra 
Tiffany,
YES PART A IS RIGHT WHAT DID YOU GET FOR PART B OF QUESTION 2

Math 116 algebra 
Karine,
I thought that maybe it would be. $175,000x+$200,000y=$7,200,000
Would this be correct? 
Math 116 algebra 
Tiffany,
yes that's right and part c and then question 3

Math 116 algebra 
Karine,
can you explain how to do the elimination part of 2c?

Math 
hannah,
42/56 in simplest form