Step 1 :Given that the salesperson received a commission of $180 for selling $1650 worth of merchandise.
Step 2 :We can calculate the commission rate by dividing the commission by the total sales and then multiplying by 100 to convert it to a percentage.
Step 3 :Let's denote the commission as \(c\), and the total sales as \(s\). The commission rate \(r\) can be calculated as follows: \(r = \frac{c}{s} \times 100\)
Step 4 :Substitute \(c = 180\) and \(s = 1650\) into the equation, we get \(r = \frac{180}{1650} \times 100\)
Step 5 :Calculate the above expression to get the commission rate \(r = 10.909090909090908\)
Step 6 :Round the commission rate to the nearest tenth of a percent to get \(r = 10.9\)
Step 7 :Final Answer: The salesperson is paid a commission rate of \(\boxed{10.9\%}\)