At Zippy Rent-a-Car, you can rent a car for $50 per day with a one-time fee of $30. At Speedy Rent-a-Car, you can rent a car for $40 per day with a one-time fee of $70. The goal is to find the number of days for which both rental locations will cost the same amount using substitution.

Answer 1

To find the number of days for which both rental locations will cost the same amount, we need to set up equations for the total cost at each location and then solve for the number of days.

Let \( d \) be the number of days for which the cars are rented.

At Zippy Rent-a-Car: The cost can be represented by the equation: \[ C_Z = 50d + 30 \] where \( 50d \) is the daily rental cost and \( 30 \) is the one-time fee.

At Speedy Rent-a-Car: The cost can be represented by the equation: \[ C_S = 40d + 70 \] where \( 40d \) is the daily rental cost and \( 70 \) is the one-time fee.

To find out when both costs are the same, we need to set the two equations equal: \[ 50d + 30 = 40d + 70 \]

Now, let's solve for \( d \) by first isolating the terms involving \( d \). Subtract \( 40d \) from both sides: \[ 50d - 40d + 30 = 70 \] This simplifies to: \[ 10d + 30 = 70 \]

Next, we can isolate \( 10d \) by subtracting 30 from both sides: \[ 10d = 70 - 30 \] This simplifies to: \[ 10d = 40 \]

Now, divide by 10 to solve for \( d \): \[ d = 4 \]

Thus, the number of days for which both rental locations will cost the same amount is \( \boxed{4} \).