Problem 28 - Prealgebra

Question

The following problems are similar to Problems \(1-22\). Set them up in the same way, but use a calculator for the calculations. Commission Rate If the commission on the sale of $$ 79.40\( worth of clothes is $$ 14.29,\) what is the commission rate? (Round to the nearest percent.)

Step-by-Step Solution

Answer

The commission rate is 18%.

Step 1: Understand the Problem

We need to find the commission rate given the total sale amount and the commission earned from this sale. The goal is to express the commission as a percentage of the total sales.

Step 2: Set Up the Equation

The commission rate can be found using the formula: \[\text{Commission Rate} = \left(\frac{\text{Commission}}{\text{Sales Amount}}\right) \times 100\%\]In this problem, the commission is \(14.29 and the sales amount is \)79.40.

Step 3: Calculate the Commission Rate

Substitute the values from the problem into the formula:\[\text{Commission Rate} = \left(\frac{14.29}{79.40}\right) \times 100\%\]Calculate the division first, then multiply by 100 to get the percentage.

Step 4: Perform the Calculation

Using a calculator, compute the value:\[\frac{14.29}{79.40} \approx 0.1799\]Now, multiply by 100 to convert this to a percentage:\[0.1799 \times 100 \approx 17.99\%\]

Step 5: Round to the Nearest Percent

Round 17.99% to the nearest whole number. Since 0.99 rounds up, the final answer is 18%.

Key Concepts

Percentage Calculation

Calculating a percentage is a common but crucial mathematical concept used in various real-life applications, like determining commission rates. It involves finding out how much one quantity represents in terms of another quantity, expressed as a part of 100.

• To calculate a percentage, you use the formula: \(\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\%\).
• "Part" refers to the specific amount you're interested in, whereas "Whole" is the total amount in context.
• The process often includes first calculating the "fraction" by dividing, then converting this fraction into a percentage by multiplying by 100.

In the exercise about commission rates, the commission earned is the "Part," and the total sales amount is the "Whole." You divide these amounts and then multiply by 100 to find the percentage. This step helps answer questions about commission directly and offers insight into the relationship between the two quantities.

Prealgebra Problems

Prealgebra problems lay the foundation for understanding algebraic concepts by focusing on arithmetic operations, basic equations, and number relationships. They are usually your first step in transitioning from simple arithmetic to more complex algebraic thinking.

• Prealgebra often involves setting up equations where one needs to find unknown values. It requires breaking problems into understandable parts and using logical steps to solve them.
• In this context, determining a commission rate involves creating an equation from known values. The prealgebra problem involves, "What percentage is the commission relative to the total sales?"
• These problems generally encourage understanding relationships between numbers rather than just finding the answer.

Through careful analysis and logical progression, prealgebra helps solve real-world problems like calculating commission rates. It enhances problem-solving skills applicable beyond just mathematics.

Calculator Usage

Using a calculator can significantly simplify solving math problems, especially those involving complex calculations like percentages. Calculators assist in performing arithmetic operations quickly and accurately, minimizing human error.

• For percentage calculations, calculators help efficiently perform division and multiplication needed to convert a fraction into a percentage.
• In the scenario of calculating a commission rate, the calculator is used to divide the commission by the total sales and multiply by 100, streamlining the computation.
• Most calculators also have functions to handle rounding numbers, which is useful when you need to round a percentage to the nearest whole number.

Accessing these functions ensures students can focus on understanding the math problem's setup rather than complex calculation processes, turning their attention to learning concepts and logic.