Math Problem Statement

Kristina receives a commission of 2.3% on her monthly sales up to $3,800. The rate then increases to 4% on the next $5,100, and the top rate of 10.1% applies to any further sales. During November, Kristina's sales were $23,421 and sales returns were $576.

a) Calculate Kristina's commission for November. $

b) Calculate her average hourly rate if she worked 32 hours during November. $

Solution

a) Calculate Kristina's commission for November

First, we need to calculate Kristina's total eligible sales for November. She made sales of $23,421, and the sales returns were $576. So, her net sales for November are:

Net Sales=23,421576=22,845\text{Net Sales} = 23,421 - 576 = 22,845

Now, we can calculate Kristina’s commission based on the three-tiered commission rate.

  1. First tier: 2.3% on sales up to $3,800
    The commission on the first $3,800 is:

Commission on first 3,800=3,800×2.3100=87.40\text{Commission on first } 3,800 = 3,800 \times \frac{2.3}{100} = 87.40

  1. Second tier: 4% on the next $5,100
    Kristina’s sales exceed $3,800, so the next $5,100 will be subject to the 4% commission rate. The commission on the second $5,100 is:

Commission on next 5,100=5,100×4100=204\text{Commission on next } 5,100 = 5,100 \times \frac{4}{100} = 204

  1. Third tier: 10.1% on the remaining sales
    After the first $3,800 and $5,100, the remaining sales are:

Remaining Sales=22,8453,8005,100=14,945\text{Remaining Sales} = 22,845 - 3,800 - 5,100 = 14,945

The commission on these remaining sales is:

Commission on remaining sales=14,945×10.1100=1,511.20\text{Commission on remaining sales} = 14,945 \times \frac{10.1}{100} = 1,511.20

Now, we add up the commissions from each tier:

Total Commission=87.40+204+1,511.20=1,802.60\text{Total Commission} = 87.40 + 204 + 1,511.20 = 1,802.60

So, Kristina’s commission for November is $1,802.60.


b) Calculate her average hourly rate

To calculate her average hourly rate, we use the total commission and divide it by the number of hours she worked in November.

Average Hourly Rate=Total CommissionHours Worked=1,802.6032=56.38\text{Average Hourly Rate} = \frac{\text{Total Commission}}{\text{Hours Worked}} = \frac{1,802.60}{32} = 56.38

So, Kristina's average hourly rate for November is $56.38.


Would you like any further details on the calculations or concepts used? Here are some related questions to explore:

  1. How would Kristina's commission change if her sales were higher than $23,421?
  2. How do tiered commission rates differ from flat commission rates in terms of income potential?
  3. How do commission structures impact employee motivation in sales?
  4. What are the pros and cons of commission-based pay versus salary-based pay?
  5. How would Kristina’s commission look if she had $0 in returns?

Tip: When calculating commissions, always break down the sales into the different brackets specified by the commission structure to avoid missing out on any higher-rate commissions.

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Commission Structure
Basic Arithmetic
Hourly Rate Calculation

Formulas

Commission on Sales = Sales Amount × Commission Rate
Net Sales = Total Sales - Sales Returns
Average Hourly Rate = Total Commission ÷ Hours Worked

Theorems

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Suitable Grade Level

Grades 10-12