The drama club sells adult tickets for $10 each and student tickets for $6 each. The club wants to collect at least $300 in ticket sales. Which inequality shows this relationship, where is the number of adult tickets sold and is the number of student tickets sold?
A two-variable inequality models a total that must meet a limit. Multiply each type's price by its own ticket count, then add the earnings. Translate “at least” as greater than or equal to, since reaching the goal counts. Keep each price paired with its own ticket type; swapping them gives the wrong total even if the inequality sign is right.
Hints
- Hint 1
The revenue from one kind of ticket is its price times the number sold. Keep the adult price with the adult count: what expression gives the money from adult tickets?
- Hint 2
A minimum is an amount you must reach or exceed. Once you add the adult and student earnings, which inequality sign includes exactly meeting the sales goal?
Step-by-step
Build the ticket-sales inequality
Step 1Find the adult-ticket earnings
No Desmos needed. The job is to translate the sales goal, not solve an equation. Each adult ticket brings in $10, and counts adult tickets, so adult-ticket earnings are dollars.
- Step 2
Find the student-ticket earnings
Each student ticket brings in $6, and counts student tickets, so student-ticket earnings are dollars.
- Step 3
Add the two kinds of earnings
The club collects money from both kinds of tickets, so its total is dollars. Don't put with : that would price student tickets as adults.
- Step 4
Include the sales goal
“At least” means equal to or greater than, so collecting exactly $300 counts: . This models the club's ticket-sales goal. Choice D.