Making realistic scenarios for the given lines

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Homework Help Overview

The discussion revolves around creating realistic scenarios that can be modeled by linear equations, specifically y = mx + b. Participants are tasked with defining variables and ensuring the scenarios are plausible.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants present scenarios involving a golf course membership and a car wash service, attempting to define variables and costs associated with each.
  • Questions arise regarding the realism of the scenarios, particularly concerning the implications of discounts and total costs.
  • Some participants question the interpretation of the equations and the meaning of the constants involved.
  • There is discussion about the necessity of a free variable in the context of fixed costs versus variable costs.

Discussion Status

Participants are actively questioning the validity of the scenarios presented, with some suggesting that the golf course example may not work as intended. There is a recognition that the equations need to produce meaningful results for various values of x, and some guidance is offered regarding the implications of fixed versus variable costs.

Contextual Notes

Participants express confusion over the definitions of total costs and discounts, particularly in relation to the stated total costs of the golf course and car wash scenarios. There is an ongoing exploration of how to accurately represent these situations within the constraints of the linear equations provided.

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Homework Statement



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

2. Homework Equations
y=mx + b

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.
 
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Kirito123 said:
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.
What happened to the $2500?
If y represents the total cost, spending 10 days leads to total "costs" of -$450?
Kirito123 said:
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.
Shouldn't you pay more for extra services if you wash your car more often? That is a cheap car wash by the way.
 
hmm aren't car washes cheap sometimes, and that would bring in more customers and make them more money?
 
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.
 
mfb said:
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.
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??
mfb said:
What happened to the $2500?
If y represents the total cost, spending 10 days leads to total "costs" of -$450
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.
 
Kirito123 said:
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??
What about some base price for providing a service in general and an additional fee based on actual use? Many systems work like that.

Kirito123 said:
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.
Same question again: What happened to the $2500? You always pay more than $1000, something your formula does not reflect.
 
wait what your saying is that I am not stating what 2500 is? since i said it was the total would that means 2500 is y since its the total amount?
 
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.
 
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.
 
  • #10
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.
 
  • #11
mfb said:
If you stay for a fixed week, then there is no free variable at all?

a free variable? sorry but isn't there not suppose to be a free variable?
 
  • #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
Kirito123 said:
wait what your saying is that I am not stating what 2500 is? since i said it was the total would that means 2500 is y since its the total amount?
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
 
  • #13
Kirito123 said:
a free variable? sorry but isn't there not suppose to be a free variable?
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.
 
  • #14
x is the total amount of days spent at the golf course right?
 
  • #15
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.
 
  • #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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