A linear cost model fits a one-time fee plus a charge for each unit. Multiply the per-unit charge by the number of units, then add the one-time fee. If the total has a limit, compare the whole cost to that limit with an inequality. Watch for multiplying the fee by the number of units or pointing the inequality the wrong way.
Hints
- Hint 1
A rate of $0.60 per mile means the charge grows by $0.60 for each mile. What expression gives the mileage charge for miles?
- Hint 2
A base fee is paid once, whether the trip is short or long. Add it to the mileage charge without multiplying it by .
- Hint 3
An inequality compares amounts that don't have to be equal. At most includes the limit itself and every amount below it. How should you compare the total charge with $12?
Step-by-step
Build the charge, then apply the limit
Step 1Write the mileage charge
No Desmos needed. You're choosing an inequality, not solving one. The app charges $0.60 per mile, so multiply $0.60 by miles to get the mileage charge:
- Step 2
Add the base fee once
The base fee is charged once, so add $1.80 to the mileage charge:
The per-mile rate multiplies ; the base fee is added once. Putting inside parentheses after would multiply the fee by the rate too.
- Step 3
Put the total below the limit
At most $12 means the charge can equal $12 or be less. Compare the total charge to that limit:
Reversing the inequality would allow charges of $12 or more. This inequality gives the allowed trip distances. Choice D.