A salesman's monthly commission is 15% on all sales over $12000. If his goal is to make a commission of at least $3000/month, what minimum monthly sales figures must he attain?
To calculate the minimum monthly sales figures the salesman must attain, we can set up an equation. Let's denote the monthly sales figures as "x."
According to the information given, the salesman's commission is 15% on all sales over $12,000. This means that for any sales amount below $12,000, he does not receive any commission.
For sales above $12,000, the commission can be calculated using the equation: Commission = 15% * (Sales - $12,000)
The salesman's goal is to make a minimum commission of $3,000 per month. Therefore, we can set up the equation:
Commission >= $3,000
Substituting the commission equation we derived earlier:
15% * (Sales - $12,000) >= $3,000
Simplifying the equation, we get:
0.15 * (Sales - $12,000) >= $3,000
Now we solve the equation to find the minimum sales figures. Let's do it step by step:
1. Divide both sides of the equation by 0.15:
(Sales - $12,000) >= $3,000 / 0.15
2. Calculate the right side of the equation:
$3,000 / 0.15 = $20,000
3. Add $12,000 to both sides of the equation:
Sales >= $20,000 + $12,000
4. Simplify:
Sales >= $32,000
Therefore, the salesman must make a minimum of $32,000 in sales per month to attain a commission of at least $3,000.
To find the minimum monthly sales figures the salesman must attain, we can set up an equation based on the given information.
Let's assume the monthly sales figures to be x.
According to the given information, the salesman's commission is 15% on all sales over $12000. This means that the commission he earns on sales above $12000 is 15% of (x - $12000).
His goal is to make a commission of at least $3000/month. So we can set up the equation as follows:
0.15(x - $12000) ≥ $3000
Now, let's solve for x:
0.15x - $1800 ≥ $3000
0.15x ≥ $3000 + $1800
0.15x ≥ $4800
Dividing both sides of the inequality by 0.15, we get:
x ≥ $4800 / 0.15
x ≥ $32000
Therefore, the salesman must attain minimum monthly sales figures of at least $32000.
$20,000 x 15%=3000
commission is for sales over $12000
$12000 + 20000= $32,000