A ticket-budget question calls for a linear inequality: an expression for the cost compared with a spending limit. Multiply each ticket price by its matching count, then add the costs. A maximum budget allows the family to spend the full amount or less. The traps are swapping the prices and treating a maximum as a minimum.
Hints
- Hint 1
A unit price is the cost of one ticket. Match each price to its ticket type before multiplying: which price goes with the number of adult tickets, and which goes with the number of child tickets?
- Hint 2
The total cost is the adult-ticket cost plus the child-ticket cost. Add the two costs, not the two ticket counts. What expression gives the family's whole bill?
- Hint 3
An upper bound is the largest amount allowed. A maximum budget permits spending exactly that amount, but not more. Which inequality sign expresses that limit?
Step-by-step
Build the ticket-cost inequality
Step 1Find the adult-ticket cost
No Desmos needed. You're translating a budget into an inequality, not solving a given equation. Each adult ticket costs $12, so adult tickets cost dollars.
- Step 2
Find the child-ticket cost
Each child ticket costs $8, so child tickets cost dollars. Don't attach the adult price to .
- Step 3
Add the costs
The family pays for both kinds of tickets, so its total cost is the sum of the two costs:
- Step 4
Apply the budget limit
A maximum budget means the total can equal $80, but cannot exceed it. Write that limit as:
So the family's ticket cost must be at most $80. Choice D.