A linear inequality can describe a cost that must stay within a budget. Multiply the per-person charge by the number of people, then add the flat fee once. Compare that total with the spending limit. The key trap is treating “no more than” as a minimum instead of an upper limit that includes the budget itself.
Hints
- Hint 1
The per-student charge grows with the number of students. Multiply the charge for one student by to get that part of the cost. Which charge stays the same as changes?
- Hint 2
An upper limit is the most the school can spend, and spending exactly that amount is allowed. Which inequality sign lets the total equal the budget but not go above it?
Step-by-step
Build the cost, then apply the limit
Step 1Find the cost that changes
No Desmos needed. You're modeling the cost, not solving for . The per-student charge is $8 for each of the students, so that part of the cost is .
- Step 2
Add the one-time bus fee
The flat fee is $120 paid once, regardless of how many students go, so the total cost is . Multiplying $120 by would charge the bus fee once per student.
- Step 3
Keep the total within the budget
“No more than” means the total can equal $400 but cannot exceed it. So put the total cost at or below the limit: . This represents the possible numbers of students. Choice B.