A fixed fee plus a per-item charge forms a linear model: each added item raises the total by the same amount, but the total does not start at zero. Turn the two orders into input-output pairs, fit a line in Desmos, and evaluate it at the requested number of items. Don't divide an order's total by its item count; that total includes the fee.
Hints
- Hint 1
A fixed fee is paid once, while the per-taco price is paid for every taco. Treat each order as a pair: the number of tacos and the total cost. What two pairs does the problem give you?
- Hint 2
In , the slope is the price per taco, and is the fee paid even for zero tacos. Both totals include the fee, so fit the two pairs to find those values.
Step-by-step
Fit and use a linear price model
Step 1Turn the orders into points
The -taco order costs , so it gives the point : tacos first, total dollars second. The -taco order gives . Each total includes the fixed fee, so dividing by would not give the price of one taco.
- Step 2
Find the price per taco and the fee
The slope means extra dollars per taco; the intercept means the charge for zero tacos. Enter the two points in a Desmos table, then type . The tells Desmos to fit the line. Under PARAMETERS, it shows and . The -dollar taco price repeats, but the -dollar fee is paid only once.
- Step 3
Find the cost for eight tacos
Type , where is the total cost for tacos, then type . Desmos prints , so 8 tacos cost $18. Choice C.