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Question 837197: A charter airline finds that on its Saturday flights from Philadelphia to London, all 120 seats will be sold if the ticket price is $200. However, for each $3 increase in ticket price, the number of seats sold decreases by one.
(a) Find a formula for the number of seats sold if the ticket price is P dollars.
(b) Over a certain period, the number of seats sold for this flight ranged between 90 and 115. What was the corresponding range of ticket prices?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 2 formulas that can be used.
the first formula solves for the price per ticket based on the number of tickets sold.
that formula is:
P = 200 + 3 * (120 - T))
if you sell 120 tickets, the price per ticket is 200.
if you sell 119 tickets, the price per ticket is 200 + (3*1) = 200 + 3 = 203.
if you sell 118 tickets, the price per ticket is 200 + (3*2) = 200 + 6 = 206.
if you sell 121 tickets, the price per ticket is 200 + (3*(-1)) = 200 - 3 = 197.
if you sell 122 tickets, the price per ticket is 200 + (3*(-2)) = 200 - 6 = 194.
the second formula solves for the number of tickets sold based on the price per ticket.
that formula is:
T = 120 - ((P - 200) / 3))
if the price per ticket is 200, the number of tickets sold is 120.
if the price per ticket is 203, the number of tickets sold is 120 - (3/3) = 120 - 1 = 119.
if the price per ticket is 206, the number of tickets sold is 120 - (6/3) = 120 - 2 = 118.
if the price per ticket is 197, the number of tickets sold is 120 - (-3/3) = 120 + 1 = 121.
if the price per ticket is 194, the number of tickets sold is 120 - (-6/3) = 120 + 2 = 122.
depending on your needs, you can use one formula or the other.
for example, question b asks:
Over a certain period, the number of seats sold for this flight ranged between 90 and 115. What was the corresponding range of ticket prices?
you would want to use the formula that gives you the price per ticket for the number of tickets sold.
that formula is:
P = 200 + 3 * (120 - T))
when T = 90, that formula tells you that the price per ticket is equal to:
200 + 3 * (120 - 90) which is equal to 200 + 3 * (30) which is equal to 200 + 90 which is equal to 290.
when T = 115, that formula tells you that the price per ticket is equal to:
200 + 3 * (120 - 115) which is equal to 200 + 3 * (5) which is equal to 200 + 15 which is equal to 215.
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