SOLUTION: Hi. I've been having trouble with this equation. There's so many steps that I cannot even figure out where I went wrong. Can you please show me step-by-step how to solve this equat

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Question 705194: Hi. I've been having trouble with this equation. There's so many steps that I cannot even figure out where I went wrong. Can you please show me step-by-step how to solve this equation and also provide an equation with variable instead of the numbers given so I know how to solve this problem with any numbers. Thanks in advance.
An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars per ticket it sells 10,000 tickets. For every 45 dollars the ticket price is reduced, an extra thousand tickets are sold. Thus if the tickets are sold for 155 dollars each then 11,000 tickets sell. It costs the airline 100 dollars to fly a person.
(a) Express the total profit P in terms of the number n of tickets sold.
(b) Express the total profit P in terms of the price p of one ticket.
(a) P(n)= _____ $
(b) P(p)= _____ $
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Using x for how many tickets sell, y for price of ticket,
________x___________y
_______10000_______$200
_______11000_______155
_______12000_______110
Slope is -9/200, and plugging any point in to figure y intercept,
.

We can find an expression or formula to determine sales in money using both x and y. From the linear equation just found, we find .
See that sales is x*y, meaning (How many tickets sold)*(ticket price) dollars.

Sales then is
The cost to fly one patron is

The profit then is Sales minus Cost, which is:
P(y)=
Notice profit here is formed as a function of how many tickets are sold (and assumed matched to the number of ticket holders flown).