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Chapter 6: Problem 9

Hillside Travel pays its employees \(\$ 10\) per hour plus 8\(\%\) commission on all trips booked. Tyrus worked 20 hours last week and booked trips amounting to \(\$ 2,100 .\) What was his gross pay for last week?

Short Answer

Expert verified
Tyrus's gross pay for last week was \$368.

Step by step solution

01

Calculate Earnings From Hours Worked

First calculate how much Tyrus made just from the hours that he worked. Since we know that he earns $10 an hour and that he worked 20 hours last week, we can multiply these two numbers together to find this part of his income. It would be \(10 * 20 = \$200\) So Tyrus earned \$200 from his hourly wage last week.
02

Calculate Commission From Booked Trips

Next, find out how much Tyrus made from his 8% commission on the trips he booked last week. Since we know that he booked \$2,100 worth of trips, we can calculate his commission by multiplying this number by 8%. Remember to convert 8% to decimal form, it would be 0.08. Therefore, the calculation would be \(2,100 * 0.08 = \$168\) So Tyrus made \$168 from commissions last week.
03

Calculate Total Gross Pay

To find out his total gross pay, we need to add each part of his earnings together. This means adding the \$200 he got from his hourly wage to the \$168 commission he received from booking trips. Therefore, the calculation would be \(200 + 168 = \$368\). So Tyrus\'s total gross pay last week was \$368.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Commission Calculation
In the realm of financial algebra, commission calculation is an essential concept. A commission is a performance-based reward typically offered to sales professionals. It provides an incentive for employees to increase sales and benefit both them and the company.
  • In the provided exercise, Tyrus earns a commission on travel bookings. This means for every trip he books, he's paid an additional percentage of the sale amount.
  • His commission is calculated as 8% of the total value of the trips booked. To find this value, convert the percentage into a decimal by dividing the number by 100 (i.e., 8% becomes 0.08).
To calculate the commission like Tyrus's, you multiply the total booked amount (\( \\(2100 \)) by 0.08, giving \(\\)168\). Simple, right? This incentivizes employees to sell more, as more sales mean more earnings.
Hourly Wage
An hourly wage is a direct compensation scheme where employees are paid a set amount for each hour worked. It ensures employees have a predictable base salary independent of variable factors such as sales.
  • Tyrus earns \(\\(10\) per hour, which is straightforward and easy to understand.
  • Working hours are added up over a week to calculate the earnings from his hourly wage.
For instance, since he worked 20 hours, we calculate his earnings by multiplying 20 hours by \(\\)10\). Hence, \(20 \times 10 = \$200\). This ensures a reliable earnings base for employees.
Gross Pay Calculation
Gross pay encapsulates total earnings before deductions like taxes or social security. It's the aggregate of all income sources a worker receives.
  • In Tyrus's case, his gross pay for the week is composed of his hourly wage plus any commissions earned during the same timeframe.
  • To compute gross pay, simply add his wage from hours worked to the commission he earned from bookings.
So, by combining the calculated hourly earnings \(\\(200\) with his commission \(\\)168\), we find that Tyrus's gross pay for the week is \(200 + 168 = \$368\). Using this straightforward method ensures accuracy and helps employees understand their earnings.
Mathematical Solution Steps
Breaking down problems into manageable mathematical solution steps enhances understanding and problem-solving skills. Here's how we applied this to Tyrus's gross pay calculation:
  • Step 1: Calculate earnings from hourly wages. Multiply hours worked by the hourly rate: \(20 \times 10 = \\(200\).
  • Step 2: Calculate earnings from sales commissions. Multiply the total sales amount by the commission rate: \(2100 \times 0.08 = \\)168\).
  • Step 3: Sum all earnings to find the gross pay. Add both components: \(200 + 168 = \$368\).
Each step is clear and methodical, ensuring that calculations are accurate and logical. By approaching problems in this step-by-step manner, complex tasks become simple, and you can ensure precision in mathematical results.

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Most popular questions from this chapter

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