A fixed fee plus a charge “per mile” signals a linear model: one amount stays the same while the other grows with the miles. Multiply the per-mile price by miles, but add the flat fee only once. Set that sum equal to the stated total. Swapping which amount is multiplied charges the pickup fee for every mile.
Hints
- Hint 1
A rate gives the cost for one mile. To find the charge for miles, multiply the rate by . Which of the two charges changes as more miles are driven?
- Hint 2
A flat fee is paid once, no matter how many miles the trip covers. Identify the term for that one-time charge before you set the fare equal to the total cost.
Step-by-step
Build the fare equation
Step 1Find the mileage charge
No Desmos needed. You’re choosing an equation, not calculating the miles.
The rate is $0.80 per mile, so for miles the mileage charge is . The per-mile price, not the pickup fee, gets multiplied by .
- Step 2
Add the pickup fee
The $3.50 pickup fee is a constant term: it doesn’t change with the miles driven. Because it’s charged once, the trip costs dollars before you match it to the given total.
- Step 3
Match the total cost
An equation says two amounts are equal. The mileage charge plus the pickup fee is the total cost, $11.30, so
That’s the equation used to find the number of miles driven. Choice C.