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) Responses 20x−50=10x−100; x=−5; after 5 days the prices are equal 20 x minus 50 equals 10 x minus 100 ; x equals negative 5 ; after 5 days the prices are equal 50+20x=100x+10; x=1; after 1 day the prices are equal 50 plus 20 x equals 100 x plus 10 ; x equals 1 ; after 1 day the prices are equal 50x+20=100x+10; x=5; after 5 days the prices are equal 50 x plus 20 equals 100 x plus 10 ; x equals 5 ; after 5 days the prices are equal 50+20x=100+10x; x=5; after 5 days the prices are equal 50 plus 20 x equals 100 plus 10 x ; x equals 5 ; after 5 days the prices are equal

Answer 1

To find out after how many days the rental car prices are equal, we can set up equations based on the information given.

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

Equation for Rental Car A: The total cost for rental car A can be expressed as: \[ \text{Cost}_A = 100 + 10x \]

Equation for Rental Car B: The total cost for rental car B can be expressed as: \[ \text{Cost}_B = 50 + 20x \]

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

Now, we can solve for \( x \):

1. Rearranging the equation: \[ 100 - 50 = 20x - 10x \] \[ 50 = 10x \]
2. Dividing both sides by 10: \[ x = 5 \]

Interpretation of the solution: The solution \( x = 5 \) means that after 5 days of rental, the costs of rental car A and rental car B will be equal. Therefore, if you rent either car for a period of more than 5 days, rental car B will be more expensive, whereas if rented for less than 5 days, rental car A will be more expensive.