Chris can be paid one of two ways. Plan A is a salary of $420 per month, plus a commission of 7% of sales. Plan B is a salary of $552 per month, plus a commission of 4% of sales. For what amount of sales is Chris better off selecting plan A?
Chris should select plan A for sales greater than$___
420 + .07(420)x > 552 + .04(552)x
Solve for x.
To determine the amount of sales for which Chris would be better off selecting plan A, we need to find the point at which the total compensation under plan A exceeds the total compensation under plan B.
Let's break down the total compensation for each plan:
For Plan A:
Salary = $420 per month
Commission = 7% of sales
For Plan B:
Salary = $552 per month
Commission = 4% of sales
To find the point at which Chris is better off selecting Plan A, we can set up the equation:
Total compensation under Plan A > Total compensation under Plan B
Let's assume the amount of sales is S.
For Plan A:
Total compensation under Plan A = Salary + Commission
= $420 + 0.07S
For Plan B:
Total compensation under Plan B = Salary + Commission
= $552 + 0.04S
Now we can set up the equation:
$420 + 0.07S > $552 + 0.04S
To solve for S (the amount of sales at which Chris is better off selecting Plan A), we can isolate the variable S:
0.07S - 0.04S > $552 - $420
0.03S > $132
S > $132 / 0.03
S > $4,400
Therefore, Chris should select Plan A for sales greater than $4,400.