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Making realistic scenarios for the given lines

  1. Apr 20, 2016 #1
    1. The problem statement, all variables and given/known data

    9. Suggest a realistic scenario that could be modelled with each of the following equations. Be sure to define each variable, including units.

    2. Relevant equations

    y=mx + b

    3. The attempt at a solution


    a. y = –65x + 200

    To stay at a private golf course, you have to pay a total of $2500. But, the private golf course has a deal that says if you purchase a membership for the golf course, which costs $200, $65 of the total cost will be deducted per day. In the equation, y represents the total cost, -65 represents the discount of the member ship (a $65 deduction), x represents the number of days spent at the golf course after purchasing the membership, and $200 is the total cost of the membership.


    b. y = 3.5x + 10

    A local car wash charges a total of $3.5 per car wash, with an additional fee for extra services. In the equations above, y represents the total cost of the car wash, 3.5 represents the total cost per car wash, x represents the number of car washes, and 10 represent the additional fee for extra services.


    I understand what I have to do and I know I'm doing it correctly, just wanted to know if the 2 examples I gave for each line made sense. Since it has to be realistic I can't have a scenario that doesn't sound realistic.
     
  2. jcsd
  3. Apr 20, 2016 #2

    mfb

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    What happened to the $2500?
    If y represents the total cost, spending 10 days leads to total "costs" of -$450?
    Shouldn't you pay more for extra services if you wash your car more often? That is a cheap car wash by the way.
     
  4. Apr 29, 2016 #3
    hmm aren't car washes cheap sometimes, and that would bring in more customers and make them more money?
     
  5. Apr 29, 2016 #4

    mfb

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    Well, google some prices. But that is not the main point I think. The additional services cost more if you wash your car more often.
     
  6. Apr 29, 2016 #5

    They do?? i hardly ever go to the car wash so i have no clue. I just made this problem up and to me it made sense. Since i can only use this formula for b to make my problem "y = 3.5x + 10", does that mean that my problem isn't realistic and i should try to make a new one??





    I think i get what you mean since if you stay longer the cost goes into negatives which means they have to pay you lol. So if i did this would that make more sense:

    (anything bold is what I added, which is pretty little)

    To stay at a private golf course for only 1 week, you have to pay a total of $2500. But, the private golf course has a deal that says if you purchase a membership for the golf course, which costs $200, $65 of the total cost will be deducted per day. In the equation, y represents the total cost, -65 represents the discount of the member ship (a $65 deduction), x represents the number of days spent at the golf course after purchasing the membership, and $200 is the total cost of the membership.
     
  7. Apr 29, 2016 #6

    mfb

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    What about some base price for providing a service in general and an additional fee based on actual use? Many systems work like that.

    Same question again: What happened to the $2500? You always pay more than $1000, something your formula does not reflect.
     
  8. Apr 29, 2016 #7
    wait what your saying is that im not stating what 2500 is? since i said it was the total would that means 2500 is y since its the total amount?
     
  9. Apr 29, 2016 #8

    mfb

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    With your golf scenario, staying for one day costs $2500+$200-$65 = $2635, staying for 7 days costs $2500+$200-7*$65 = $2245
    None of those values match your function y = –65x + 200, which predicts y=135 for x=1 and y=70 for x=2.
     
  10. Apr 29, 2016 #9
    wait i think you might have misunderstood, staying for 1 week not 1 day. so it would be $2500 + $200 - 65 = $2635 this is for the whole week you stay.
     
  11. Apr 29, 2016 #10

    mfb

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    If you stay for a fixed week, then there is no free variable at all?

    You said "$65 of the total cost will be deducted per day", that would indicate 7*$65 for a week.



    That golf scenario won't work.
     
  12. Apr 29, 2016 #11
    a free variable? sorry but isn't there not suppose to be a free variable?
     
  13. Apr 29, 2016 #12
    Car wash:
    Y can equal the car wash price.
    Would it work if you switched the explanation for m and b
    I'd like going to the carwash more if the extra services cost less than the actual wash. It would make me want to get multiple extra services.

    I think scrapping the golf course idea would be quicker than trying to make it fit
    Here you say y=2500
    10 is what mfb used so x=10 for 10 stays at the course
    2500=-65(10)+200
    2500=-650+200
    2500=-450
     
  14. Apr 29, 2016 #13

    mfb

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    In the "you have to book 1 week at the golf course", what is x?
    You have a function "y as function of x", that doesn't make much sense if there is only one possible value of x.
     
  15. Apr 29, 2016 #14
    x is the total amount of days spent at the golf course right?
     
  16. Apr 29, 2016 #15

    mfb

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    Then your function would have to produce meaningful results for e. g. x=1.
    1 day spent at the golf course => y = 200-65*1 = 135. So who pays $135?

    As I said before, the golf course example for that equation does not work. Try to understand why it does not work, but it won't get fixed.
     
  17. Apr 29, 2016 #16
    O i see so i will forget the whole thing in general and start a new problem that makes sense.
     
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