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 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

Answer 1

To determine after how many days the costs of rental cars A and B will be equal, we can start by setting up equations for the total cost of each rental car.

1. For Rental Car A:

   • Initial cost: $100
   • Daily cost: $10 per day
   • Total cost after $x$ days: $${\text{Cost}}_A=100+10x$$

2. For Rental Car B:

   • Initial cost: $50
   • Daily cost: $20 per day
   • Total cost after $x$ days: $${\text{Cost}}_B=50+20x$$

To find when the costs are equal, we set the two equations equal to each other: $$100+10x=50+20x$$

Now, we can solve 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: $$x=5$$

The interpretation of the solution $x=5$ means that after 5 days, the rental costs of both cars will be equal.

To verify, we can calculate the total cost for both cars after 5 days:

• For Car A: $${\text{Cost}}_A=100+10(5)=100+50=150$$

• For Car B: $${\text{Cost}}_B=50+20(5)=50+100=150$$

Both costs come out to $150, confirming that our solution is correct.

Answer 2

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

20x−50=10x−100; x=−5; after 5 days the prices are equal

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

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

Answer 3

To find when the costs of Rental Car A and Rental Car B are equal, let's formulate the equation based on the provided rates:

1. Rental Car A:

   • Initial cost: $100
   • Daily cost: $10 per day
   • Total cost after $x$ days: $${\text{Cost}}_A=100+10x$$

2. Rental Car B:

   • Initial cost: $50
   • Daily cost: $20 per day
   • Total cost after $x$ days: $${\text{Cost}}_B=50+20x$$

Next, we set the two total costs equal to find $x$: $$100+10x=50+20x$$

Now, let's solve this equation step by step:

1. Rearranging the equation:

   • 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

The solution $x=5$ means that after 5 days, the rental costs for both car A and car B will be equal.

Verifying the Solution

To ensure accuracy, we can compute the total costs for both cars after 5 days:

• For Car A: $${\text{Cost}}_A=100+10(5)=100+50=150$$

• For Car B: $${\text{Cost}}_B=50+20(5)=50+100=150$$

Both Car A and Car B will have a total cost of $150 after 5 days, confirming that our calculated solution $x=5$ is correct.

Equation and Solution Reference

From the responses provided, the correct equation is:

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

This matches the numbers and solution we verified through the calculations.