Question

Cars-4-Rent charges a $75 deposit and $17.00 per mile when renting a car. Auto-Rent charges $100 deposit and $12.00 per mile when renting a car. Write an inequality that shows how many miles, m, you would have to go for Cars-4-Rent to cost more than Auto-Rent.

Answer 1

To determine when Cars-4-Rent is more expensive than Auto-Rent, an inequality is set up comparing each company's cost per mile and fixed deposit. The inequality 75 + 17m > 100 + 12m is solved to find that Cars-4-Rent is more expensive after more than 5 miles.

Step-by-step explanation:

To determine when Cars-4-Rent would cost more than Auto-Rent, we need to set up an inequality comparing the total cost of renting a car from each company.

The cost for Cars-4-Rent is a $75 deposit plus $17.00 per mile, which can be expressed as the cost function C(m) = 75 + 17m, where m represents the number of miles.

Similarly, the cost for Auto-Rent is a $100 deposit plus $12.00 per mile, which can be expressed as A(m) = 100 + 12m.

To find when Cars-4-Rent is more expensive than Auto-Rent, we set up the following inequality:

75 + 17m > 100 + 12m

Solving for m:

• Subtract 75 from both sides: 17m > 25 + 12m
• Subtract 12m from both sides: 5m > 25
• Divide both sides by 5: m > 5

Therefore, Cars-4-Rent will cost more than Auto-Rent when you rent the car for more than 5 miles.