Math Problem Statement
Mike can be paid in one of two ways based on the amount of merchandise he sells:
Plan A: A salary of $900.00 per month, plus a commission of 9% of sales, OR Plan B: A salary of $1,100.00 per month, plus a commission of 11% of sales in excess of $9,000.00.
For what amount of monthly sales is plan B better than plan A if we can assume that Mike's sales are always more than $9,000.00? Write your answer an an inequality involving x, where x represents the total monthly sales.
Solution
We are asked to determine the sales amount for which Plan B is better than Plan A. Let's break this down:
Plan A:
- Salary: $900 per month
- Commission: 9% of total sales
- Total earnings under Plan A:
where is the total monthly sales.
Plan B:
- Salary: $1,100 per month
- Commission: 11% of sales in excess of $9,000
- Total earnings under Plan B:
[ E_B = 1
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
Plan A earnings: E_A = 900 + 0.09x
Plan B earnings: E_B = 1100 + 0.11(x - 9000)
Theorems
Linear inequality principles
Suitable Grade Level
Grades 9-11