An inequality models ticket sales that must reach at least a target, rather than match it exactly. Add the money from each ticket type; a given ticket count makes one part fixed. Use a Desmos regression on the equality to find the cutoff, then choose the first whole ticket count above it. A fractional cutoff isn't a number of tickets you can sell.
Hints
- Hint 1
The revenue is the money collected from sales. Multiply each ticket price by the number of that kind sold, then add the two amounts. Which part is already fixed by the 60 student tickets?
- Hint 2
The boundary is the adult-ticket count that would make sales equal the goal exactly. Find that count, then use at least to decide which way to move to reach a whole number of tickets.
Step-by-step
Find the revenue cutoff
Step 1Write the ticket-sales inequality
Let be the number of adult tickets. Adults bring in dollars, and the 60 student tickets bring in dollars. At least $1,300 means the total can equal or exceed $1,300, so the inequality is
- Step 2
Find where sales reach the goal
The boundary is where sales equal the goal. Type in Desmos. The asks Desmos to find the value of that makes the sides equal; stands for the adult-ticket count. Under PARAMETERS, Desmos shows the cutoff . The in the inequality means counts at or above that cutoff meet the goal.
- Step 3
Choose the smallest whole ticket count
Tickets come in whole numbers, so adult tickets isn't possible. For an at least goal, take the first whole number above a fractional cutoff. That's , not . The center must sell a minimum of adult tickets. Grid in 47.