Write an equation and interpret the solution to the following problem: Rental car A has a rate of an initial $100, plus $10 per day. Rental car B has a rate of an initial $50, plus $20 per day. After how many days are the rental car prices equal?(1 point)

1 answer

To find the number of days at which the rental car prices are equal, we can set up an equation based on the costs of renting each car.

Let \( x \) represent the number of days rented.

The cost for rental car A can be expressed as: \[ \text{Cost of A} = 100 + 10x \]

The cost for rental car B can be expressed as: \[ \text{Cost of B} = 50 + 20x \]

To find when the costs are equal, we set the two equations equal to each other: \[ 100 + 10x = 50 + 20x \]

Now, we can solve the equation for \( x \).

  1. Subtract \( 10x \) from both sides: \[ 100 = 50 + 10x \]

  2. Subtract \( 50 \) from both sides: \[ 50 = 10x \]

  3. Divide both sides by \( 10 \): \[ x = 5 \]

Interpretation of the Solution:

The solution \( x = 5 \) means that after 5 days, the rental cost of car A will be equal to the rental cost of car B. Specifically, at this point, both cars will cost the same amount to rent:

  • Cost of Car A after 5 days: \( 100 + 10(5) = 100 + 50 = 150 \)
  • Cost of Car B after 5 days: \( 50 + 20(5) = 50 + 100 = 150 \)

Thus, both rental cars will cost $150 after 5 days of rental.