Question

Write an inequality to model the situation when renting a car from Car-Rent-A-Center with two payment options:

Option A: $25 a day plus 150 a mile
Option B: $10 a day plus 400 a mile
For what amount of daily miles will option A be the cheaper plan?

Answer 1

To find out when Option A is cheaper than Option B for renting a car, we set up an inequality (25 + 0.15m < 10 + 0.40m) and solve for m. Option A is cheaper when driving more than 60 miles a day.

Step-by-step explanation:

To determine for what amount of daily miles Option A would be the cheaper plan when comparing car rental plans from Car-Rent-A-Center, we can set up an inequality. Let's denote the number of miles driven per day as m.

For Option A, which costs $25 per day plus $0.150 per mile, the daily cost will be 25 + 0.15m. For Option B, which costs $10 per day plus $0.400 per mile, the daily cost will be 10 + 0.40m.

We are looking for when Option A is cheaper than Option B, so our inequality will be:

25 + 0.15m < 10 + 0.40m

To solve for m, we follow these steps:

1. Subtract 0.15m from both sides: 25 < 10 + 0.25m
2. Subtract 10 from both sides: 15 < 0.25m
3. Divide both sides by 0.25: m > 60

Hence, Option A will be the cheaper plan when the daily miles driven are more than 60 miles.