Question

Translate to an equation and solve. Wright earns \(10 \%\) of total sales in commission. If he sells \(\$ 3106\) in merchandise over a two-week period, what is his commission?

Short answer

Answer: Wright's commission is $310.60.

Step-by-step solution

Convert the percentage to a decimal

To convert a percentage to a decimal, we simply need to divide the percentage value by 100. In this case, Wright earns 10% in commission, so we will divide 10 by 100: 10/100 = 0.1

Calculate the commission

Now that we know the decimal equivalent of the commission percentage (0.1), we can multiply this by the total sales amount to find out Wright's commission. The total sales amount is $3106, so we will multiply 0.1 by 3106: 0.1 * 3106 = 310.6

Express the commission in dollars

We have calculated the commission to be 310.6. This is already in dollars, so we can simply write down the result. Wright's commission is: \$ 310.6

Key concepts

Commission Calculation

When it comes to understanding commission, it's important to recognize that it is a form of compensation often used in sales, where an employee or agent earns a percentage of the sales they make. In the case of Wright, his commission is 10% of the total sales amount. To calculate his earnings, we need to convert this percentage into a workable figure.

When a commission is given as a percentage, it represents the portion of the total sales that will be the individual's earnings. To find the exact dollar amount Wright earns, we convert his 10% commission rate into a decimal by dividing by 100. Then, we multiply this decimal by the total sales to calculate the actual earnings. For example: if Wright sells $3106 worth of merchandise, multiplying this value by 0.1, the decimal equivalent of 10%, gives us his commission in dollars. It's an essential skill in business and personal finance to be able to perform these calculations accurately.

Applying Percentages

Understanding how to apply percentages is crucial in various real-world scenarios, such as calculating discounts, interest rates, and commissions, like in Wright's situation. The process of applying percentages begins by converting the percentage into a decimal. This is done to simplify multiplication since it's more straightforward to multiply by a decimal than a percentage.

To convert a percentage to a decimal, divide the percentage by 100. For instance, 10% becomes 0.10. This conversion is the crucial step before applying the percentage to any numerical value. After conversion, the decimal can be multiplied with the total figure to compute the portion represented by the percentage. Remember, the outcome represents the same part of the whole as the original percentage does, whether it’s a portion of sales, like with commissions, or a part of any other quantity.

Basic Algebra

At the heart of commission calculations and applying percentages lies basic algebra. It's a branch of mathematics that involves working with numbers and variables to solve equations. Solving algebraic equations often requires a systematic approach, wherein we isolate the variable we're trying to solve for.

The problem with Wright's commission is a simple algebraic equation in nature. We are given a total sales amount and a commission rate; we want to find the commission in dollars. By setting up an equation with the commission as the unknown variable, multiplying the total sales by the commission rate expressed as a decimal, we can solve for the unknown. This process of forming an equation from a word problem, isolating the variable, and then solving for it is a fundamental algebraic skill. Moreover, understanding these basics allows one to apply algebra in various practical and financial contexts.