To address Part A, let's carefully analyze the given rational expression [tex]\(\frac{200x - 300}{x}\)[/tex].
The expression [tex]\(\frac{200x - 300}{x}\)[/tex] is used to model the average profit per watch sold. To understand what the numerator [tex]\(200x - 300\)[/tex] represents, let's break it down step by step:
1. The expression [tex]\(200x\)[/tex]:
- Here, [tex]\(x\)[/tex] represents the number of watches sold.
- The number 200 represents the revenue generated from selling each watch.
- Therefore, [tex]\(200x\)[/tex] is the total revenue obtained from selling [tex]\(x\)[/tex] watches.
2. The expression [tex]\(-300\)[/tex]:
- The number -300 represents the initial or fixed costs incurred by Ian's business, such as production costs, rent, salaries, or other overheads.
By combining these two parts, we get:
[tex]\[ 200x - 300 \][/tex]
So, the numerator [tex]\(200x - 300\)[/tex] represents the total profit minus initial costs:
- [tex]\(200x\)[/tex] is the total revenue generated from selling [tex]\(x\)[/tex] watches.
- [tex]\(-300\)[/tex] subtracts the fixed costs from that total revenue.
Thus, the numerator [tex]\(200x - 300\)[/tex] represents "the total profit minus initial costs" for Ian's business.
Therefore, the numerator of the rational expression [tex]\(\frac{200x - 300}{x}\)[/tex] specifically represents:
[tex]\[ \text{The total profit minus initial costs (with \(200x\) representing total revenue and \(-300\) representing fixed costs).} \][/tex]
