You rent a car for $25 per day with a one time fee of $100 at zippy rent a car but at speedy rent a car you can rent a car for $30 per day with a one time fee of $30. Write and solve the system of equations to find the number of days for which both car rental locations will cost the same

Answer 1

To find the number of days for which both car rental locations will cost the same, we can set up equations based on the given rental rates and fees.

Let \( d \) be the number of days of rental.

Cost of renting from Zippy Rent A Car:

• Daily rate: $25 per day
• One-time fee: $100

The total cost for renting from Zippy can be expressed as: \[ C_Z = 25d + 100 \]

Cost of renting from Speedy Rent A Car:

• Daily rate: $30 per day
• One-time fee: $30

The total cost for renting from Speedy can be expressed as: \[ C_S = 30d + 30 \]

Setting the costs equal to find \( d \):

We want to find the number of days \( d \) such that the costs are the same: \[ 25d + 100 = 30d + 30 \]

Solving the equation:

1. Subtract \( 25d \) from both sides: \[ 100 = 5d + 30 \]

2. Subtract 30 from both sides: \[ 70 = 5d \]

3. Divide both sides by 5: \[ d = \frac{70}{5} = 14 \]

Conclusion:

The two car rental locations will cost the same after 14 days.