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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 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 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 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 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 Skip to navigation

5 answers

Let's start by forming the equations based on the rental car rates.

  1. Rental car A: The total cost is given by the initial fee plus the daily rate multiplied by the number of days (\(x\)): \[ \text{Cost of Car A} = 100 + 10x \]

  2. Rental car B: Similar to car A, the total cost is: \[ \text{Cost of Car B} = 50 + 20x \]

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

  2. Subtract 50 from both sides: \[ 100 - 50 = 10x \] \[ 50 = 10x \]

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

Interpretation of the solution:

The solution \(x = 5\) means that after 5 days, the total rental costs of car A and car B will be equal. At this point, both options would cost the same amount to rent, allowing a renter to decide based on factors other than price, such as the type of vehicle or specific rental policies.

whats the answer

The correct answer to the problem is:

The equation is: \[ 100 + 10x = 50 + 20x \]

The solution is: \[ x = 5 \]

Interpretation: After 5 days, the rental prices of both car A and car B are equal.

i gave you 4 options you didnt pick one

I apologize for not selecting the correct option from your provided choices. The correct option based on the solution is:

50 + 20x = 100 + 10x; x = 5; after 5 days the prices are equal.

Thank you for your patience, and I'm here if you have any more questions!