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

Question

At Zuli Rent a car you can rent a movie for 25 dollars per day which a one time fee of 100 dollars at speedy rent a car you can rent a car for 30 dollars per day with a one time fee of 30 write and solve a system of equations to find the number of days fr 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 a system of equations based on the information provided:

Let \( x \) represent the number of days rented.

1. Zuli Rent a Car: The total cost can be expressed as: \[ C_1 = 100 + 25x \]

2. Speedy Rent a Car: The total cost can be expressed as: \[ C_2 = 30 + 30x \]

To find the number of days when the costs are equal, we can set the two equations equal to each other: \[ 100 + 25x = 30 + 30x \]

Now, we will solve for \( x \).

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

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

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

So, the number of days for which both car rental locations will cost the same is 14.