Question

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