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)
50 + 20x = 100х + 10; x = 1; after 1 day the prices are equal
20х - 50 = 10x - 100;
• x = -5; after 5 days the prices are equal
• 50 + 20x = 100 + 10х; x = 5; after 5 days the prices are equal
• 50х + 20 = 100х + 10; x = 5;
after 5 days the prices are equal

Answer 1

Short answer

Answer 2

Choose one
50 + 20x = 100х + 10; x = 1; after 1 day the prices are equal
20х - 50 = 10x - 100;
• x = -5; after 5 days the prices are equal
• 50 + 20x = 100 + 10х; x = 5; after 5 days the prices are equal
• 50х + 20 = 100х + 10; x = 5;
after 5 days the prices are equal

Answer 3

To determine when the rental car prices are equal, we can set up the equations based on the rental car rates.

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

**For Rental Car A**:
The cost is given by the equation:
\[
\text{Cost}_A = 100 + 10x
\]

**For Rental Car B**:
The cost is given by the equation:
\[
\text{Cost}_B = 50 + 20x
\]

Next, we set these two equations equal to find the point of intersection (when the costs are the same):
\[
100 + 10x = 50 + 20x
\]

Now, let's solve for \( x \):

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

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

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

### Interpretation of the Solution:
The solution \( x = 5 \) indicates that after 5 days of rental, the costs of Rental Car A and Rental Car B will be equal. Specifically, both cars will cost the same amount to rent after 5 days.

- **Cost of Rental Car A after 5 days**:
\[
\text{Cost}_A = 100 + 10 \times 5 = 100 + 50 = 150
\]

- **Cost of Rental Car B after 5 days**:
\[
\text{Cost}_B = 50 + 20 \times 5 = 50 + 100 = 150
\]

Thus, both cars will cost $150, confirming that our solution is correct.

Answer 4

To find when the rental car prices are equal, we set up the equation:

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

Solving this gives:

\[
50 = 10x \implies x = 5
\]

**Interpretation**: After 5 days, the costs of Rental Car A and Rental Car B will be equal, at $150 each.

Answer 5

The correct equation and interpretation is:

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