SOLUTION: Please help, I began solving letter see, but I'm not sure if it is correct. In most businesses, increasing prices of products can negatively impact the number of customers. A bu

Question 77478: Please help, I began solving letter see, but I'm not sure if it is correct.
In most businesses, increasing prices of products can negatively impact the number of customers. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.
a. Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function, and find the slope of the graph.
b. The bus company determined that even if they set the price very low, there are a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?
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 by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.
:
a. Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function, and find the slope of the graph.
:
Let x = cost of the bus ride; Let y = number of customers per day
:
Lets say they increase the fare to $3 then the number of customers would be
800 - (3*40) = 680; x1 = 3; y1 = 680
:
Lets say they increase the fare to $4 then the number of customers would be
800 - (7*40) = 520; x2 = 4; y2 = 520
:
Find the slope using these coordinates:
m = (520 - 680)/(4 - 3) = -160 is the slope
:
Find the equation using the point/slope equation: y - y1 = m(x - x1)
y - 680 = -160(x - 3)
y - 680 = -160x + 480
y = -160x + 480 + 680
y = -160x + 1160
:
The graph should look like this:

:
b. The bus company determined that even if they set the price very low, there are a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?
:
You can see from the equation that when x = 0 (ride free), 1160 passengers would ride.
:
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?
:
That would be the x intercept, (y = 0)
-160x + 1160 = 0
-160x = -1160
x = -1160/-160
x = $7.25 would the fare when no one would be riding You can also see this on the graph
:
A good check is to substitute the original fare for x, (2.25) and check to see
that y = 800
:
How about this? Did it help you understand this problem?

RELATED QUESTIONS
I can not figure out this problem, please help: In most businesses, increasing prices of... (answered by checkley71)

Could you please help me solve this question. I did some of it. Thank you It is not... (answered by ankor@dixie-net.com)

Can you please help me with this question I am very confused by it. I am clueless.... (answered by jim_thompson5910)

Please help. If 10 ounces of flour = 2.3 cups, how many cups are in 100 ounces of... (answered by josgarithmetic,MathTherapy)

I am having trouble writing this statement using mathmatical symbols I didnt see the... (answered by stanbon)

Anyone help me with solving this equation please? x-7/7 = x-3/5 I am getting -7 but... (answered by Alan3354)

My son has statements that he needs to write the inequality using symbols for each... (answered by stanbon)

I have to evaluate the binomial (2y-1)^2 I get 2y^2+1 but am not sure if it is right.... (answered by stanbon)

the sum of two numbers is 25. one number is less than three times the other number. find... (answered by algebrahouse.com)