A moving company charges a flat fee of $120 plus $25 per hour of work. If a customer can spend no more than $350 on the service, which inequality models the possible number of hours, , that the company can work for the customer?
A charge that combines a flat fee with an hourly rate leads to a linear inequality when there’s a spending limit. Multiply the hourly rate by the hours, then add the fee paid once. “No more than” means the total can equal the limit but cannot exceed it. Reversing the inequality would allow bills over budget.
Hints
- Hint 1
The hourly rate is the amount charged for each hour. Multiply the number with “per hour” attached to it by to find the part of the bill that changes with time.
- Hint 2
A flat fee is paid once, even if the work takes several hours. Add it to the hourly charge without multiplying it by . What expression represents the whole bill?
- Hint 3
An upper limit tells you how high the bill can go. “No more than” includes the exact budget and every smaller cost, so use , not .
Step-by-step
Build the bill, then apply the limit
Step 1Find the hourly charge
No Desmos needed. You’re choosing a model, not solving for the hours. The company charges $25 per hour, so multiply that rate by hours to get the hourly part of the bill: dollars.
- Step 2
Add the one-time fee
The $120 flat fee is charged once, not once per hour. Add it to the hourly charge to get the total cost in dollars: . Multiplying by would give the one-time fee the wrong job.
- Step 3
Apply the budget limit
“No more than $350” means the total can be $350 or less. This is an inclusive upper limit, so write: . That inequality models the possible hours the company can work within the customer’s budget. Choice D.