Answer:
If the tickets are priced at $20 each, the total amount of money taken in would be $88,000.
Explanation:
To write the number of tickets sold, n, as a function of the ticket price, p, we can use the given information that for every $1 increase in price, 200 tickets go unsold.
Let's define the slope of the line as the decrease in tickets per dollar increase in price. Since 200 tickets go unsold for every $1 increase, the slope of the line is -200.
Now, let's find the equation of the line through the given points: (12, 6000), (13, 5800), (14, 5600), and so on.
Using the point-slope form of a linear equation, we have:
n - 6000 = -200(p - 12)
Simplifying the equation, we get:
n - 6000 = -200p + 2400
Rearranging the equation to solve for n, we have:
n = -200p + 8400
This equation represents the number of tickets sold, n, as a function of the ticket price, p.
To find how much money will be taken in if the tickets are $20 each, we substitute p = 20 into the equation:
n = -200(20) + 8400
n = -4000 + 8400
n = 4400
If the tickets are $20 each, the number of tickets sold would be 4400. To calculate the total amount of money taken in, we multiply the number of tickets sold by the ticket price:
Money taken in = Number of tickets sold * Ticket price
Money taken in = 4400 * $20
Money taken in = $88,000
Hope this helps.