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)

Answer 1

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.