Question

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

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

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

Answer 1

To find the number of days after which the rental car prices of A and B are equal, we can set up the following equation based on their pricing models.

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

For rental car A:
- Initial cost = $100
- Daily rate = $10
- Total cost after \( x \) days = \( 100 + 10x \)

For rental car B:
- Initial cost = $50
- Daily rate = $20
- Total cost after \( x \) days = \( 50 + 20x \)

Now we can set the two equations equal to each other to find when their costs are the same:

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

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

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

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

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

Thus, the solution is \( x = 5 \).

**Interpretation of the solution:**
After 5 days of rental, the total costs of rental car A and rental car B will be equal.