To find the range of total revenue for the car dealership's sales of 48 cars in one month, we need to consider the average price of the car along with its maximum variance and then calculate the minimum and maximum possible revenue.
1. Determine the lowest and highest possible prices for a single car:
- The average price of each car is [tex]$25,000.
- The price variance is $[/tex]3,000.
- The lowest possible price for a car = average price - price variance = [tex]$25,000 - $[/tex]3,000 = [tex]$22,000.
- The highest possible price for a car = average price + price variance = $[/tex]25,000 + [tex]$3,000 = $[/tex]28,000.
2. Calculate the total revenue for the minimum and maximum prices:
- There are 48 cars sold.
- Minimum total revenue = number of cars sold × lowest possible price = 48 × [tex]$22,000 = $[/tex]1,056,000.
- Maximum total revenue = number of cars sold × highest possible price = 48 × [tex]$28,000 = $[/tex]1,344,000.
3. Determine the range of total revenue:
- Combining the minimum and maximum total revenues calculated, we get the range as [tex]$1,056,000 \leq x \leq $[/tex]1,344,000.
Thus, the correct answer is:
D. [tex]$\$[/tex] 1,056,000 \leq x \leq \[tex]$ 1,344,000$[/tex]
