Question

you are planning a business trip on which you will drive 200 miles over a period of 2 days. you need to rent a car for the trip. auto express charges $20.00 per day plus 10c per mile driven. galaxy rent a car charges $27.50 per day with no charge for mileage. using the company with the lowest rate, how much will it cost to rent the car?
a $20.00
b $27.50
c $40.00
d $55.00
e $60.00

Explanation:

Step1: Calculate cost for Auto Express

Auto Express charges $20 per day plus 10¢ per mile. For 2 days and 200 miles:
Daily cost: \( 20 \times 2 = 40 \) dollars.
Mileage cost: \( 0.10 \times 200 = 20 \) dollars.
Total for Auto Express: \( 40 + 20 = 60 \) dollars? Wait, no—wait, recheck. Wait, Galaxy Rent A Car: $27.50 per day, no mileage. For 2 days: \( 27.50 \times 2 = 55 \) dollars. Wait, the question says "using the company with the lowest rate". Let's recalculate both:

Auto Express:
Daily: \( 20 \times 2 = 40 \)
Mileage: \( 0.10 \times 200 = 20 \)
Total: \( 40 + 20 = 60 \)? Wait, no, wait the options: E is $60, D is $55. Wait, Galaxy: \( 27.50 \times 2 = 55 \). Auto Express: \( 20*2 + 0.10*200 = 40 + 20 = 60 \). So Galaxy is cheaper? Wait, no, the question says "Auto Express charges $20 per day plus 10c per mile. Galaxy Rent A Car charges $27.50 per day with no charge for mileage. Using the company with the lowest rate, how much will it cost to rent the car?"

Wait, Auto Express total: \( 20 \times 2 + 0.10 \times 200 = 40 + 20 = 60 \). Galaxy: \( 27.50 \times 2 = 55 \). So 55 is lower? Wait, but the options: D is $55, E is $60. Wait, maybe I misread. Wait, the problem: "You are planning a business trip on which you will drive 200 miles over a period of 2 days. You need to rent a car for the trip. Auto Express charges $20.00 per day plus 10c per mile driven. Galaxy Rent A Car charges $27.50 per day with no charge for mileage. Using the company with the lowest rate, how much will it cost to rent the car?"

So calculate both:

Auto Express:
Cost = (daily rate × days) + (mileage rate × miles)
= \( (20 × 2) + (0.10 × 200) \)
= \( 40 + 20 = 60 \) dollars.

Galaxy:
Cost = daily rate × days
= \( 27.50 × 2 = 55 \) dollars.

55 is less than 60, so Galaxy is cheaper. So the cost is $55, which is option D? Wait, but the options: A:20, B:27.50, C:40, D:55, E:60. Wait, no—wait, maybe I messed up the days. Wait, 2 days: Galaxy is 27.50 × 2 = 55. Auto Express: 20×2=40, plus 0.10×200=20, total 60. So 55 is lower, so the answer is D: $55.00? Wait, but let's re-express:

Wait, the problem says "using the company with the lowest rate". So compare the two totals:

Auto Express: 2 days × $20 + 200 miles × $0.10 = $40 + $20 = $60.

Galaxy: 2 days × $27.50 = $55.

Since $55 < $60, the lowest rate is Galaxy, so cost is $55. So the answer is D.

Step2: Confirm the lower cost

Auto Express total: \( 20 \times 2 + 0.10 \times 200 = 60 \).
Galaxy total: \( 27.50 \times 2 = 55 \).
55 is less than 60, so choose Galaxy's cost, which is $55.

Answer:

D. $55.00