Making realistic scenarios for the given lines

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.

 

hmm aren't car washes cheap sometimes, and that would bring in more customers and make them more money?

 

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.

 

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?

 

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.

 

a free variable? sorry but isn't there not suppose to be a free variable?

 

x is the total amount of days spent at the golf course right?

 

O i see so i will forget the whole thing in general and start a new problem that makes sense.