A car rental agency charges $150 per week plus $0.1 per mile to rent a car. How many miles can you travel in one week for $170 ?
The correct answer and explanation is:
To determine how many miles can be traveled for $170, we need to break down the total cost. The rental agency charges a fixed amount of $150 per week plus $0.10 for every mile traveled.
Let’s denote the number of miles traveled as xx. The total cost of renting the car for a week, including mileage, can be represented by the equation: Total cost=150+0.10x\text{Total cost} = 150 + 0.10x
We know that the total cost for the week is $170, so we can set up the equation: 170=150+0.10×170 = 150 + 0.10x
Now, subtract 150 from both sides to isolate the term with xx: 170−150=0.10×170 – 150 = 0.10x 20=0.10×20 = 0.10x
Next, divide both sides of the equation by 0.10 to solve for xx: 200.10=x\frac{20}{0.10} = x x=200x = 200
So, you can travel 200 miles in one week for a total cost of $170.
Explanation
The rental agency charges a base fee of $150 for the week. To this base cost, a fee of $0.10 is added for each mile traveled. Given that you have a total of $170 to spend, the amount available for the mileage charge is the difference between $170 and $150, which is $20. Since each mile costs $0.10, you can calculate the number of miles by dividing $20 by $0.10, which gives you 200 miles. Thus, you can drive 200 miles for the $170 cost, covering both the base rental and the mileage charges.