A salesman may draw a fixed salary of $10000 per month and a 2% commission sales or he can draw a fixed salary of $4000 per month and a 12% commission on sales.what volume of sales would he earn him the same amount of money in both rates??pls explain the answer
let the sales be s
solve for s:
.12s + 4000 = .02s + 10000
To determine the volume of sales that would earn the salesman the same amount of money in both rates, we need to set up an equation and solve for the sales amount.
Let's denote the volume of sales as "x" (in dollars).
For the first scenario with a fixed salary of $10,000 per month and a 2% commission on sales, the earnings can be calculated using the formula:
Earnings1 = Fixed Salary + Commission
Earnings1 = $10,000 + 0.02x
For the second scenario with a fixed salary of $4,000 per month and a 12% commission on sales, the earnings can be calculated as:
Earnings2 = Fixed Salary + Commission
Earnings2 = $4,000 + 0.12x
To find the sales volume that would result in the same earnings in both scenarios, we set Earnings1 equal to Earnings2 and solve for x:
$10,000 + 0.02x = $4,000 + 0.12x
First, let's isolate the variable terms on one side of the equation:
0.02x - 0.12x = $4,000 - $10,000
-0.10x = -$6,000
Now, divide both sides of the equation by -0.10 to solve for x:
x = (-$6,000) / (-0.10)
x = $60,000
Therefore, the salesman would earn the same amount of money in both rates if his volume of sales amounts to $60,000.
It's important to note that this calculation assumes that the salesman's salary remains fixed regardless of the sales volume and that the commission is applied only to the amount of sales.