Help me understand how to make a eqation out of story problem please?

In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.


The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?


Answer:





Show work in this space:





c) If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?





Answer:





Show work in this space:

Help me understand how to make a eqation out of story problem please?
First of all you have to make the wide-sweeping assumption that the number of customers lost or gained is a linear function of the price. Assuming this...





You need to find a function R = f(P), where P is the price and R is the number of riders. You have one point, namely (P,R) = (2.00, 1000). Assume that f(P) = mP+b, as is usual for a linear function. Then





1000 = m(2)+b





You are given that if P is increased by 0.25, then R is decreased by 50. This means that another point is given by (P,R) = (2.00+0.25,1000-50) = (2.25,950). So





950 = m(2.25) + b





Solve these two equations for m and b. Do this yourself before continuing to read. You should get:





R = 1400-200P.





The first question can't be answered. Sure, you can plug in 0 for P and get R = 1400, but how do you know they don't permit, say, only 1300 riders? The problem does not say. If so, the answer is not 1400, but 1300.





To answer the second question, labeled c), you need to substitute 0 for R and solve for P. You should get P = $7. Would you pay $7 for a bus fare? I wouldn't.
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Reply:If an increase of 25 cents causes 50 people to stop riding, then a decrease of 25 cents should cause 50 more people to ride. Therefore, you need to find out how many more people will ride when you decrease it by 200 cents.


200/25 = 8, so a decrease of the fare to nothing will mean 8 reductions of 25 cents, and 8 *50 people will start riding. In other words, it is 200 * (50 / 25) more people, or 400 more people, for a total of 1400 people.








The rate of change of people per cent increase is


(- 50 people) / (25 cents) = -2 (people / cent)


If we want the number of people to be zero, divide the number of more people you want to start riding the bus by this rate, and you will get a value in cents. Since you want to find when 1000 people stop riding the bus, you need to use -1000, or a decrease of 1000 people, for the number of people.


Then 1000/2 = 500, or 500 cents, which is 5 dollars more, or 7 dollars.