A linear model fits a charge made of a one-time fee plus a constant amount for every mile. Let a variable count miles, multiply it by the per-mile rate, and add the fee once to match the total. Then use a one-variable Desmos regression to find the miles. The tempting slip is stopping at the mileage charge in dollars.
Hints
- Hint 1
An unknown is the quantity you’re trying to find. Let count miles. Since each mile costs the same amount, what expression gives the mileage charge, in dollars, for miles?
- Hint 2
The flat fee is paid once, however many miles Mason drives. Add it to the mileage charge and set the sum equal to the total. Which part of that equation should contain ?
Step-by-step
Model the total charge and solve
Step 1Write the mileage charge
Let mean the miles driven. The rate is $0.20 for each mile, so miles cost dollars. That’s the mileage charge, not the total.
- Step 2
Match the charge to the total
The $55 flat fee is paid once, and Mason’s total is $87, so . Multiply the rate by miles, but add the flat fee only once.
- Step 3
Find the miles in Desmos
Type . Replace with and with so Desmos solves for the unknown instead of offering a slider. Under PARAMETERS, it shows . Since counts miles, Mason drove 160 miles. Choice B.