A salesman's monthly commission is 15% on all sales over $10,000. If his goal is to make a commission of at least $3600/month, what minimum monthly sales figures must he attain?
0.15x = 3600
x = 3600/0.15
x = 24,000
10,000 + 24,000 = ?
34,000
Well, to figure out the minimum monthly sales figures, we need to do a little math. Let's assume "x" represents the monthly sales figure.
First, we need to determine the sales figure that is above $10,000. We can do this by subtracting $10,000 from the monthly sales figure: x - $10,000.
Next, we multiply the sales figure above $10,000 by the commission rate of 15%: 0.15(x - $10,000).
We want to find the minimum monthly sales that will give the salesman a commission of at least $3600. So we set up the equation:
0.15(x - $10,000) ≥ $3600.
Now, let's solve for "x":
0.15x - $1500 ≥ $3600.
Adding $1500 to both sides gives:
0.15x ≥ $5100.
Dividing both sides by 0.15, we get:
x ≥ $34,000.
Therefore, the salesman must attain a minimum monthly sales figure of $34,000 to meet his goal of making a commission of at least $3600 per month. But remember, this is just the minimum figure. He can always aim higher and go for the sky!
To find the minimum monthly sales figures, we can set up an equation based on the given information.
Let's assume the monthly sales figure to be x (in dollars).
According to the given information, the salesman's commission is 15% on all sales over $10,000. So, his commission would be calculated as follows:
Commission = 15% of (x - $10,000)
In order to earn a commission of at least $3600/month, we can set up the following equation:
Commission ≥ $3600
15% of (x - $10,000) ≥ $3600
0.15(x - $10,000) ≥ $3600
Now, let's solve the equation to find the minimum monthly sales figure.
0.15(x - $10,000) ≥ $3600
0.15x - $1500 ≥ $3600
0.15x ≥ $5100
Divide both sides of the equation by 0.15:
x ≥ $34,000
Therefore, the salesman must attain a minimum monthly sales figure of at least $34,000 to earn a commission of at least $3600/month.
To find the minimum monthly sales figures that the salesman must attain, we can use the following steps:
Step 1: Determine the minimum commission amount
The salesman's goal is to make a commission of at least $3600 per month. This is the minimum commission amount the salesman needs to earn.
Step 2: Calculate the sales amount that corresponds to the minimum commission amount
Since the commission is calculated as 15% on all sales over $10,000, we need to find the sales amount that corresponds to the minimum commission amount.
Let X be the minimum sales amount that generates a commission of $3600.
The minimum commission amount can be expressed as:
$3600 = 0.15 * (X - $10,000)
Simplifying the equation:
$3600 = 0.15X - 0.15 * $10,000
$3600 + 0.15 * $10,000 = 0.15X
$3600 + $1500 = 0.15X
$5100 = 0.15X
Step 3: Calculate the minimum monthly sales figures
To find the minimum monthly sales figures, divide both sides of the equation by 0.15:
$5100 / 0.15 = X
X = $34,000
Therefore, the salesman must attain a minimum monthly sales figure of $34,000 to make a commission of at least $3600.