To determine when the rental car prices are equal, we can set up the equations based on the rental car rates.
Let \( x \) be the number of days rented.
For Rental Car A: The cost is given by the equation: \[ \text{Cost}_A = 100 + 10x \]
For Rental Car B: The cost is given by the equation: \[ \text{Cost}_B = 50 + 20x \]
Next, we set these two equations equal to find the point of intersection (when the costs are the same): \[ 100 + 10x = 50 + 20x \]
Now, let's solve for \( x \):
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Subtract \( 10x \) from both sides: \[ 100 = 50 + 10x \]
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Subtract 50 from both sides: \[ 50 = 10x \]
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Divide by 10: \[ x = 5 \]
Interpretation of the Solution:
The solution \( x = 5 \) indicates that after 5 days of rental, the costs of Rental Car A and Rental Car B will be equal. Specifically, both cars will cost the same amount to rent after 5 days.
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Cost of Rental Car A after 5 days: \[ \text{Cost}_A = 100 + 10 \times 5 = 100 + 50 = 150 \]
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Cost of Rental Car B after 5 days: \[ \text{Cost}_B = 50 + 20 \times 5 = 50 + 100 = 150 \]
Thus, both cars will cost $150, confirming that our solution is correct.