Word Problem Please help?

Question

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. The conducted a survey of their customers and found that they will lose approxinately 50 customers per day for each $.25 increase in fare. Given the description above, graph the function, identify the graph of the function, find the slope of the graph, find the price at which there will be no more riders, and find the maximun number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the 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? 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 1

no of customers=-50(0.25n)+1000
where n is element of natural numbers

Answer 2

Let x = bus fare, y = average # of riders per day.

We are told that at $2.00, we have 1000 riders per day. We are also told that if the fare increases by $0.25, then the number of riders will decrease by 50. We can therefore write down the following two ordered pairs: (2, 1000) and (2.25, 950). Using these two points, we find the slope (difference of y's over difference of x's) to be -200. Plugging into the point slope formula: y = m(x-x1) + y1 yields y = -200x + 1400. This is the relationship between x (fare) and y (# of riders). This should be easy enough to graph since you have two points and the graph is a line.

The slope = -200 which is interpreted as saying that every time x increases by 1 (i.e., everytime the fare increases by $1) y decreases by 200 (i.e., you lose 200 passengers). Note that this is the same thing as saying that when the fare increases by 0.25, you lose 50 passengers. In other words, -50/0.25 = -200/1.

The price at which there will be no more riders means that y = 0. Plugging this into y = -200x+1400 gives: 0 = -200x + 1400 or 200x=1400 or x= 7. At a fare of $7, there will be no more riders.

If the price is free (i.e., x=0), there will be y = -200(0) + 1400 = 1400 riders each day.

Answer 3

My Solution:
For every increase in price of 25 cents the loss in customers is 50 thus the graph will contain the following points:
(2, 1000) (2.25, 950) (2.5, 900) (2.75, 850) (3, 800)
The slope is (change in y)/ (change in x) thus m = -50/0.25 = -200.
Using y = mx + b, we have y = -200x + b and using the first point to find “b”, we have 1000 = -200(2) + b therefore 1000=-400 + b and b = 1400. The equation for the graph would be y=-200x+1400. When x = 0 “FREE” the y-value is 1400, thus When there is a zero price to customers using a linear progression in price they should have an average of about 1400 customers per day. To find the price at which no one will ride we set y=0 and find that 0=-200x+1400 and x=7. This means that at $7 per ticket we expect no one to ride. I could not figure out how to graph this on my computer but using the Sope-intercept graph above, you should be able to do so pretty simply. Have a great day!