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.