Write and solve a system of equations. Only write the number, not the word days

Question

At ZIppy rent a car, you can rent a car for 25$ per day, which a one time free of 100$. At Speedy rent a car, you can rent a car for 30$ per day, with a one time fee of 30$ Write and solve a system of equations to find the number of days for which both car rental locations will cost the same.

Answer 1

Let \( x \) represent the number of days you rent the car.

For Zippy Rent a Car, the total cost (\( C_1 \)) can be expressed as: \[ C_1 = 25x + 100 \]

For Speedy Rent a Car, the total cost (\( C_2 \)) can be expressed as: \[ C_2 = 30x + 30 \]

To find the number of days for which both rental locations will cost the same, we set the two equations equal to each other: \[ 25x + 100 = 30x + 30 \]

Now, we can solve for \( x \):

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

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

3. Divide both sides by 5: \[ x = 14 \]

Thus, the number of days for which both car rental locations will cost the same is 14. The solution is \( x = 14 \).