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.

Key concepts

Understanding Percentage Calculations

When dealing with discounts, percentages play a critical role. A percentage is simply a way to express any number as a fraction of 100. To apply a discount to a price, we calculate the percentage value of that price and then subtract it from the original amount.

For example, if we have a television that costs \( \\(545 \) and it's offered at an \( 8\% \) discount, we first need to find \( 8\% \) of \( \\)545 \). This is done by multiplying the price by the percentage (in decimal form): \( \$545 \times 0.08 \).

That gives us the discount amount, which can then be subtracted from the original price to find the discounted price. This calculation is essential for anyone working with discounts, sales, or even tipping at a restaurant! It's a fundamental skill in many areas of personal finance.

Reaching a Sales Quota

A sales quota is a specific sales target assigned to a salesperson, usually measured over a set period. For Robert, his goal is to achieve \( \$100,000 \) in total sales. It means that from all the televisions he sells, the cumulative sales should equal or exceed this target.

Quotas are common in sales jobs as they drive salespeople to reach and even outdo their goals. Understanding how much needs to be sold to meet this quota involves dividing the quota by the price of a single item after discounts have been applied.

Once the discounted price of the television is calculated, Robert can work out how many units he needs to sell. This forms a base for strategy and motivation, pushing towards achieving that desirable figure in sales.

Determining Minimum Quantity

The minimum quantity in this context refers to the least number of units Robert needs to sell to meet his sales target. It's essential because it provides a clear, quantifiable goal.

By dividing the sales quota by the discounted price of the television, Robert gets a number. In his case, the result was \( 199.52 \). Since Robert can't sell a fraction of a TV, he needs to round up to the nearest whole number, meaning he must sell at least \( 200 \) televisions.

This calculation not only influences Robert's daily sales targets but also helps with inventory management and forecasting. Whether in retail or broader business contexts, determining the minimum quantity is crucial for setting realistic, achievable sales goals.