Question

Mike can be paid in one of two ways based on the amount of merchandise he sells:Plan A: A salary of $800.00 per month, plus a commission of 12% of sales, ORPlan B: A salary of $950.00 per month, plus a commission of 15% of sales in excess of $9,000.00.For what amount of monthly sales is plan A better than plan B if we can assume that Mike's sales are always more than $9,000.00? Write your answer an an inequality involving X, where Xrepresents the total monthly sales

Answer 1

Step 1:

Monthly sale = $x

Where x > 9,000

Step 2:

Plan A

`\begin{gathered} \text{Salary = \$800.00} \\ \text{Commission is 12\% of \$x } \\ \text{Commission = }(12)/(100)\text{ }*\text{ x} \\ =\text{ \$0.12x} \\ \text{Monthly salary = 0.12x + 800} \end{gathered}`

Step 3

Plan B

`\begin{gathered} \text{Salary = \$950.00} \\ \text{Commission = 15\% of (x - 9000)} \\ =\text{ }(15x)/(100)\text{ - }(15*9000)/(100) \\ =0.15x\text{ - 135} \\ \text{Monthly salary = 0.15x - 1350 + 950} \\ =\text{ 0.15x }-\text{ 400} \end{gathered}`

Final answer

The amount of monthly sales that plan A better than plan B

`\begin{gathered} \text{0}.12x\text{ + 800 > 0.15x - 400} \\ 0.15x\text{ - 0.12x < 800 + 400} \\ 0.03x\text{ < 1200} \\ \text{x < }(1200)/(0.03) \\ \text{x < \$40,000} \end{gathered}`

Final answer

x < 40000