Let \( x \) represent the number of days you rent the car from Zippy Rent-A-Car, and let \( y \) represent the number of hours you rent the car from Speedy Rent-A-Car.
The cost for renting from Zippy Rent-A-Car can be expressed as: \[ C_Z = 25x + 100 \]
For Speedy Rent-A-Car, the cost can be expressed as: \[ C_S = 30y + 30 \]
To find when the costs are equal, we set the two equations equal to each other: \[ 25x + 100 = 30y + 30 \]
Now, we need to express one variable in terms of the other. Let's solve for \( y \): \[ 25x + 100 - 30 = 30y \] \[ 25x + 70 = 30y \] \[ y = \frac{25x + 70}{30} \]
This equation relates the number of days rented with the number of hours rented.
To solve the system, we can set values for \( x \) (number of days) and find corresponding \( y \) (number of hours). However, since one represents days and the other hours, we should assume a specific value for either \( x \) or \( y \).
Let's determine when it might make sense to rent for a certain number of days. Assume we want to rent for 2 days: \[ x = 2 \] Substituting into the equation: \[ y = \frac{25(2) + 70}{30} = \frac{50 + 70}{30} = \frac{120}{30} = 4 \]
Thus, renting a car for 2 days at Zippy Rent-A-Car costs the same as renting for 4 hours at Speedy Rent-A-Car.
To check: Cost at Zippy: \[ C_Z = 25(2) + 100 = 50 + 100 = 150 \]
Cost at Speedy: \[ C_S = 30(4) + 30 = 120 + 30 = 150 \]
Both costs are equal at $150.
Therefore, the system of equations has been solved with \( x = 2 \) and \( y = 4 \), meaning renting a car for 2 days at Zippy Rent-A-Car costs the same as renting for 4 hours at Speedy Rent-A-Car.
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