To determine after how many days the costs of rental cars A and B will be equal, we can start by setting up equations for the total cost of each rental car.
-
For Rental Car A:
- Initial cost: $100
- Daily cost: $10 per day
- Total cost after \( x \) days: \[ \text{Cost}_A = 100 + 10x \]
-
For Rental Car B:
- Initial cost: $50
- Daily cost: $20 per day
- Total cost after \( x \) days: \[ \text{Cost}_B = 50 + 20x \]
To find when the costs are equal, we set the two equations equal to each other: \[ 100 + 10x = 50 + 20x \]
Now, we can solve for \( x \):
-
Subtract \( 10x \) from both sides: \[ 100 = 50 + 10x \]
-
Subtract 50 from both sides: \[ 50 = 10x \]
-
Divide both sides by 10: \[ x = 5 \]
The interpretation of the solution \( x = 5 \) means that after 5 days, the rental costs of both cars will be equal.
To verify, we can calculate the total cost for both cars after 5 days:
-
For Car A: \[ \text{Cost}_A = 100 + 10(5) = 100 + 50 = 150 \]
-
For Car B: \[ \text{Cost}_B = 50 + 20(5) = 50 + 100 = 150 \]
Both costs come out to $150, confirming that our solution is correct.