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)

Question

Responses

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

50+20x=100x+10; x=1; after 1 day the prices are equal

Answer 1

Let:

• \( A \) be the total cost of rental car A after \( x \) days.
• \( B \) be the total cost of rental car B after \( x \) days.

The costs can be defined as:

• For rental car A: \( A = 100 + 10x \)
• For rental car B: \( B = 50 + 20x \)

To find out when the prices are equal, we set the two equations equal to each other:

\[ 100 + 10x = 50 + 20x \]

Now, we solve for \( x \):

1. Subtract \( 10x \) from both sides:

\[ 100 = 50 + 10x \]

2. Subtract 50 from both sides:

\[ 50 = 10x \]

3. Divide by 10:

\[ x = 5 \]

So the solution is \( x = 5 \), which means after 5 days, the prices of rental car A and rental car B are equal.

Interpretation

The conclusion is that after 5 days of rental, the total cost of both rental car A and rental car B will be the same.