SOLUTION: 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 20 dollars the ticket price is reduc

Question 1054799: 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 20 dollars the ticket price is reduced, an extra thousand tickets are sold. Thus if the tickets are sold for 180 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.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Look first at how revenue relates to price.

price      Count Sold Tickets
 200         10000
 180         11000            ---- here, i=1
 160         12000
200-20i      10000+1000i

i is used to count increments of $20.

You may want to express that price .

COST for flying 1 person was given as $100, for ONE PERSON.

KEY IDEA: P=r-c, PROFIT is revenue minus cost, but understand cost will be for all ticket buyers who are to fly.

As your description gives, P is for profit and p is for price of a ticket.

(a) profit in terms of number of tickets sold;

n for count of tickets

---------No way getting away from the unknown ticket price. Otherwise you could simply say .
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