Question

A car rental company offers two plans for renting a car. Plan A: $20 per day and $0.16 per mile. Plan B: $50 per day with free unlimited mileage. What inequality represents the situation where plan B saves you money compared to plan A? Put the expression for Plan A on the left and the expression for Plan B on the right. Use m to represent the number of miles the rental car is driven.

Answer 1

The inequality that shows when Plan B saves money over Plan A is 20 + 0.16m > 50, where m represents the miles driven. Plan B is more economical if the cost under Plan A exceeds the flat rate of Plan B.

Step-by-step explanation:

The inequality that represents the situation where Plan B saves you money compared to Plan A is when the total cost of Plan A is greater than Plan B. To determine this, we need to set up an inequality with the expression for Plan A on the left and the expression for Plan B on the right. Using m to represent the number of miles driven:

20 + 0.16m > 50

This inequality says that if the cost of renting the car with Plan A, which includes a $20 per day fee plus $0.16 per mile (0.16m), is greater than the $50 per day flat rate of Plan B, then Plan B is the more economical choice. Our variable m stands for the number of miles driven. As the number of miles increases, the total cost under Plan A also goes up. The breakeven point is where these two costs would be the same. However, if we want Plan B to save money, then the number of miles driven must be such that Plan A costs more than Plan B.