Math Problem Statement

A salesperson will receive a graduated commission that pays them 2.4% on the first $100,000 in sales, 3.2% on the next $200,000, and 4.7% on additional sales in a month. What is the average commission rate on sales for a month totaling?

Solution

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Math Problem Analysis

Mathematical Concepts

Percentage Calculations
Weighted Averages
Piecewise Functions

Formulas

Commission on first $100,000 = 100,000 * 2.4%
Commission on next $200,000 = 200,000 * 3.2%
Commission on additional sales (S > $300,000) = (S - 300,000) * 4.7%
Total Commission = Commission1 + Commission2 + Commission3
Average Commission Rate = (Total Commission) / (Total Sales)

Theorems

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Suitable Grade Level

Grades 9-12