Question 59·Medium·Linear Functions
A ride-sharing company charges a booking fee of $2.90 plus $1.80 per mile traveled.
What is the total cost, in dollars, for a customer who travels 14 miles?
For linear cost problems, quickly identify the fixed part (like a booking fee) and the variable part (cost per mile, per hour, etc.). Write a simple expression of the form , substitute the given quantity, and do the arithmetic carefully, making sure not to drop the fixed fee or mis-add the decimals.
Hints
Identify the two parts of the cost
There is a fixed booking fee and a variable cost that depends on the number of miles. Write both parts separately.
Write an expression for the total cost
Try to write the total cost as: (booking fee) (cost per mile) (number of miles). What numbers go in each place?
Calculate in two stages
First find the total cost of 14 miles at $1.80 per mile. Then add the booking fee to that result.
Desmos Guide
Use Desmos to compute the total cost
In Desmos, type the expression 2.90 + 1.80*14 exactly as given by the situation. Look at the numerical result that Desmos outputs; that value is the total cost in dollars.
Step-by-step Explanation
Translate the situation into an expression
The company charges a fixed booking fee plus a charge for each mile.
- Booking fee: $2.90
- Per-mile charge: $1.80 per mile
- Miles traveled: 14
So the total cost can be written as:
Find the cost of the miles
First calculate the cost for traveling 14 miles at $1.80 dollars per mile.
Break it up:
Add these:
Add the booking fee to the mileage cost
Now add the fixed booking fee to the mileage cost:
Add the decimals carefully:
So the total cost for a customer who travels 14 miles is $28.10, which corresponds to choice D.