A car rental company charges dollars per day for the first 3 days of a rental and 80% of that daily rate for each additional day. Sam rented a car for 5 days, and the total rental charge before taxes was $230.
What is the company’s regular daily rental rate?
A rental with one rate for the first few days and another rate afterward calls for a one-variable equation. Count the days at each rate, add their charges, and match the given total. Then use a Desmos regression to find the regular rate. The main trap is applying the discount to every day rather than only the additional days.
Hints
- Hint 1
A daily rate is the cost for one day. First count how many of Sam’s five days come after the three days charged at the regular rate.
- Hint 2
A percent means out of one hundred, so of is . Use that discounted daily rate only for the additional days. What do both parts of the rental cost together?
Step-by-step
Model the two daily rates
Step 1Count the additional days
Sam rented the car for days, and the first have the regular rate. Subtract to find the additional days:
- Step 2
Write the total charge
The first days cost dollars. A percent means out of , so , and the additional days cost dollars. Only the additional days get the discounted rate. Add both charges and match the before-tax total:
- Step 3
Find the regular daily rate
Type in Desmos. The tells Desmos to use a regression to find the value that makes both sides equal. Under PARAMETERS, it shows . Since is the regular daily rate, the company charges $50 per day before the additional-day discount. Choice C.