Question

For a special movie premiere, the theater owner decided to charge $20 per ticket for the first r rows of the theater and $15 for the remaining rows. 2. Explain how you could find the owner's total income if you knew the value of r and you knew that all tickets were sold. 3. Suppose r=16. A. Find the income in the first r rows if all of the tickets were sold. B. Find the income in the remaining r rows if all of the tickets were sold. C. Find the total income for r=16. 4. Write and simplify an expression for the owner's profit if tickets are priced at $20 per ticket in the first r rows and $15 per ticket in the remaining rows, if all seats are sold. 5. Evaluate the expression you wrote in Question 4 for r=16 and show that the result equals your answer in Question 3c.

Answer 1

Answer & Step-by-step explanation:

2. Total income = Income from first r rows + Income from other last rows

[(Price per first r rows' seat ) x (no of first r rows) x (no of seats per first r row) ] + [ (Price per other last rows' seat ) x (no of last rows) x (no of seats per last row) ]

= [ 20 x (r) x (no of seats per first r row) ] + [ 15 x (other last ie 'total - r' rows) x no of seats per last row

3. 20 x 16 x (no of seats per first r row) = 320 x (no of seats per first r row)

4. 15 x (other last ie 'total - 16' rows) x no of seats per last row