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.