Solve the problem.
-At $10 per ticket, the Casper Coyotes will fill all 7000 seats in the assembly hall. The manager knows that for every $1 increase in the price, 100 tickets will go unsold. Write the number of tickets sold, n, as a function of the
Ticket price, p. How much money will be taken in if the tickets are $15 each? Hint: Find the equation of the line
Through (10, 7000), (11, 6900), (12, 6800), etc.
A) n = -200p - 15,000; -$18,000
B) n = -100p - 7100, -$8600
C) n = -100p + 8000; 6500
D) n = 200p + 1700; $4700

Question

Quizplus · Accepted Answer

The correct equation for the number of tickets sold, $n$, as a function of the ticket price, $p$, is found by recognizing the pattern that for each $1 increase in price, 100 fewer tickets are sold. Starting from 7000 tickets at $10 each, the slope of the line connecting the points given (price, tickets sold) is $-100$ (since for every $1 increase, tickets sold decrease by 100). To find the y-intercept, we can use one of the points, for example, $p = 10$ and $n = 7000$, and solve for $b$ in the equation $n = -100p + b$. Substituting $p = 10$ and $n = 7000$ gives $7000 = -100(10) + b$, leading to $b = 8000$. Thus, the equation is $n = -100p + 8000$.To find the total money taken in when tickets are $15 each, substitute $p = 15$ into the equation to find $n$, which gives $n = -100(15) + 8000 = 6500$ tickets sold. The total money taken in is then $6500 \times 15 = \$97,500$, which is not explicitly one of the choices, indicating a misunderstanding in the question's final part. However, the correct equation and the number of tickets sold at $15 each are given in option C.

Solve the Problem. -At $10 Per Ticket, the Casper Coyotes Will Fill All