Math Problem Statement

Commission: 10 percent on first $5,000.00; 15 percent over $5,000.00; Find the total graduated commission on $22,000.00.

Solution

To calculate the graduated commission on $22,000.00, follow these steps:

  1. First $5,000: 5,000×0.10=5005,000 \times 0.10 = 500

  2. Remaining amount: 22,0005,000=17,00022,000 - 5,000 = 17,000 Now calculate 15% of the remaining $17,000: 17,000×0.15=2,55017,000 \times 0.15 = 2,550

  3. Total commission: 500+2,550=3,050500 + 2,550 = 3,050

So, the total graduated commission on $22,000 is $3,050.00.

Would you like more details on how this type of commission calculation works?

Here are five related questions:

  1. How would the commission change if the percentage over $5,000 increased to 20%?
  2. What would be the total commission if the amount was $10,000?
  3. How do you calculate commissions with more than two rate brackets?
  4. How can commission structures affect sales incentives?
  5. How would commission be calculated if there was no tiered structure?

Tip: In commission structures, the base threshold is critical in determining how much of the higher percentage will apply. Always ensure clarity on which part of the amount is affected by each rate.

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Math Problem Analysis

Mathematical Concepts

Percentages
Graduated Commission
Basic Algebra

Formulas

First part commission = base_amount × base_rate
Remaining commission = (total_amount - base_amount) × higher_rate
Total commission = base_commission + remaining_commission

Theorems

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Suitable Grade Level

Grades 9-12