Question

Robert is selling televisions at an electronics store. The televisions normally cost \(\$ 545\) each but are being sold at an \(8 \%\) discount. What is the minimum number of televisions Robert must sell if he wants to meet his quota of \(\$ 100,000\) in total sales?

Short answer

Robert must sell at least 200 televisions to meet his quota of \$100,000 in total sales.

Step-by-step solution

Calculate the discounted price of one television

To find the discounted price, we first need to find the amount of discount for one television. The discount is \(8\%\) of the original price: Discount = \(\$ 545 \times \frac{8}{100}\) Calculate the discount: Discount = \(\$ 545 \times 0.08 = \$ 43.6\) Now, we subtract the discount from the original price to get the discounted price: Discounted Price = Original Price - Discount Discounted Price = \(\$ 545 - \$ 43.6 = \$ 501.4\) The discounted price of one television is \( \$ 501.4\).

Calculate the minimum number of televisions Robert needs to sell

To find the minimum number of televisions Robert needs to sell, we will divide the total sales quota by the discounted price of one television: Minimum Number of Televisions = \(\frac{\text{Total Sales Quota}}{\text{Discounted Price of One Television}}\) Plug in the values: Minimum Number of Televisions = \(\frac{\$100,000}{\$501.4} \approx 199.52\) Since Robert cannot sell a fraction of a television, he needs to sell at least 200 televisions to meet his quota of $100,000 in total sales.