Chris can be paid in one of two ways. Plan A is a salary of $380 per month, plus a commission of 9% of sales. Plan B is a salary of $656 per month, plus a commission of 3% of sales. For what amount of sales is Chris better off selecting plan A?
Let x = amount of sales
380 + .09x = 656 + .03x
.06x = 276
x < 4600
x > 4600
To determine for what amount of sales Chris is better off selecting Plan A, we need to compare the total earnings under each plan.
Let's denote the sales amount as x.
Under Plan A, the total earnings will be the sum of the salary ($380) and the commission (9% of sales):
Total earnings under Plan A = $380 + 0.09x
Under Plan B, the total earnings will be the sum of the salary ($656) and the commission (3% of sales):
Total earnings under Plan B = $656 + 0.03x
Now we can set up the inequality to find the sales amount for which Plan A is better:
Total earnings under Plan A > Total earnings under Plan B
$380 + 0.09x > $656 + 0.03x
Now we can simplify the inequality:
0.09x - 0.03x > $656 - $380
0.06x > $276
Divide both sides of the inequality by 0.06:
x > $276 / 0.06
x > $4,600
Therefore, for sales amounts greater than $4,600, Chris is better off selecting Plan A.
To determine at what amount of sales Chris will be better off selecting Plan A, we need to compare the total earnings under both plans.
In Plan A, Chris will receive a salary of $380 per month and a commission of 9% of sales.
In Plan B, Chris will receive a salary of $656 per month and a commission of 3% of sales.
Let's start by finding the total earnings under each plan for a given amount of sales.
Total earnings under Plan A = Salary + Commission
Total earnings under Plan A = $380 + 9% of sales
Total earnings under Plan B = Salary + Commission
Total earnings under Plan B = $656 + 3% of sales
To find the amount of sales for which Chris would be better off selecting Plan A, we need to set the total earnings under Plan A equal to the total earnings under Plan B.
$380 + 9% of sales = $656 + 3% of sales
Now, let's solve this equation to find the amount of sales:
9% of sales - 3% of sales = $656 - $380
0.06 * sales = $276
sales = $276 / 0.06
sales ≈ $4,600
Therefore, Chris would be better off selecting Plan A if the amount of sales exceeds $4,600.