Question

Bryan, who works in a high-end jewelry store, earns a base pay of \(\$ 10.00\) per hour plus a certain percent commission on the sales that he helps to broker in the store. Bryan worked an average of 35 hours per week over the past two weeks and helped to broker sales of \(\$ 5,000.00\) worth of jewelry during that same two-week period. If Bryan's earnings for the two-week period were \(\$ 850.00\), what percent commission on sales does Bryan earn? A) \(1 \%\) B) \(2 \%\) C) \(3 \%\) D) \(4 \%\)

Short answer

1. Bryan's total base pay for 2 weeks: \(Total\ Base\ Pay = 2 \times (35\ hours \times \$10.00) = \$ 700.00\) 2. Bryan's commission earned during the two-week period: \(Commission = \$ 850.00 - \$ 700.00 = \$ 150.00\) 3. Determine Bryan's commission rate: \(Commission\ Rate = \frac{\$ 150.00}{\$ 5000.00} = 0.03\) \(Commission\ Rate \% = 0.03 \times 100 \% = 3 \% \) The correct answer is C) $3 \%$.

Step-by-step solution

Calculate Bryan's total base pay for 2 weeks

Since Bryan works 35 hours a week and earns a base pay of $10.00 per hour, his weekly base pay can be calculated as: \(Base Pay = Hours\ per\ week \times Hourly\ Rate\) For two weeks, the total base pay will be: \(Total\ Base\ Pay = 2 \times (35\ hours \times \$10.00)\)

Calculate Bryan's commission earned during the two-week period

Once we have Bryan's total base pay, we need to find the commission he earned during the two-week period. To do this, we will subtract the total base pay from his total earnings: \(Commission = Total\ Earnings - Total\ Base\ Pay\)

Determine Bryan's commission rate

Finally, to find the percentage commission that Bryan earns, we need to divide the commission he earned by the total sales made during the two weeks: \(Commission\ Rate = \frac{Commission}{Total\ Sales}\) Now we'll convert this commission rate to a percentage by multiplying it by 100: \(Commission\ Rate \% = Commission\ Rate \times 100 \%\) Choose the correct option among the given choices (A, B, C, D) by comparing the calculated commission rate percentage.

Key concepts

Percent Commission Calculation

Understanding percent commission calculation is essential, not just for SAT math problems, but also for real-world financial literacy. A commission is a fee paid to an employee for conducting a transaction or service, typically a percentage of the amount sold. To calculate percent commission, you need to know two key numbers: the total amount of sales and the commission earned from those sales.

The formula to find the commission rate (as a decimal) is:
\[ Commission\ Rate = \frac{Commission\ Earned}{Total\ Sales} \] And to express this as a percentage, simply multiply by 100:
\[ Commission\ Rate\ \% = Commission\ Rate \times 100 \% \]
When solving these types of problems, pay close attention to the units involved and ensure they are consistent. For instance, confirm that you're comparing earnings and sales over the same period. Avoid common pitfalls by double-checking your calculations and by remembering to convert your final decimal result into a percentage. Incorporating these methods will strengthen your understanding and ability to solve percent commission problems.

SAT Problem Solving

In tackling SAT math problems, problem-solving skills are paramount. The SAT Math section tests your ability to analyze and work through problems in a logical and methodical manner. Begin by carefully reading the problem to understand what's being asked. Then, identify the relevant information and the operations needed to find the solution.

A step-by-step approach is often the best way to ensure no detail is overlooked. For instance, when presented with a commission problem like Bryan's, break it down:

• Calculate base pay.
• Determine additional commission earnings.
• Find the percentage of the commission.

Each step is a building block that leads to the final answer. It's also a good practice to review all steps to see if there's a more straightforward method to reach the solution or to confirm the accuracy of your calculations. By enhancing your problem-solving techniques, you'll be more adept at tackling various SAT math challenges.

SAT Math Strategies

Effective SAT math strategies go beyond understanding formulas and operations; they're about optimizing your test-taking approach. Time management, for example, is crucial. Spend too much time on a single problem and you may rush through others, increasing the chance of errors.

Build a strong foundation in the mathematical basics to improve speed and efficiency. Quick recall of multiplication tables, exponent rules, and an understanding of percentages will serve you well. Practice with a variety of SAT problems to become familiar with the question formats and problem types you'll encounter.

Moreover, learn to recognize when to guess. The SAT does not penalize for wrong answers, so educated guesses can work in your favor. Eliminating one or more incorrect answers to increase your odds of guessing correctly is a helpful strategy.

Remember, practice is key. The more problems you work through, the quicker and more accurate you'll become. As you practice, always reflect on why an answer choice is right or wrong, which will deepen your understanding and improve your performance on the actual test.