Word problem: A bus company has 1000 riders per day....

[pooh27]

I am need some help withgetting a problem started. If you could help me with the formula I should be ok from there. The problem is:

A bus company has 1000 riders per day. The fare is $2.00 per ride. This company has done a survey and found that they will lose approximately 50 riders per day for each $.25 increase in fare.

With this information I need to find the slope of the graph. This is where I am having the problem. Any help would be a big help with the formula.

Thank you

 

[jwpaine]

let x be the increase in fair

income = 1000(2) - 50(x/.25)

so if you increased the fair by 1 dollar, people would drop by 50(1/0.25) = 200

so your slope is -50(x/0.25) = -200x

The max people you can have in one day is 1000(2), so in slope intercept form, this could be written as:

y = -200x + 1000(2)

as you can see, you will have a decrease in person for each increase in x


EDIT: Skeeter shows how to find money.... I made a mistake on this and needed to edit it, I would have given a similar answer, but gave people instead of money..after coming back to the computer I forgot the main purpose- which would probably be to find amount of money- not people.... oh well... here my post stands

Should have noticed sooner.



John

 

[skeeter]

your post says "slope of the graph" ... graph of what specifically?

from the information given, the following can be determined ...

let x = fare increase in dollars

individual ride price in dollars = 2 + x

number of riders = 1000 - 50(x/.25)

revenue in dollars, R = [1000 - 50(x/.25)](2 + x)

simplify R ...

R = 200(10 + 3x - x²)

note that revenue is a quadratic function with a variable "slope".

fyi, a ticket price of $3.50 will maximize revenue.