A local salesman receives a base salary of $575 monthly. If his total sales receipts for the month exceed $1800, he also receives a commission of 11% on the portion of sales over $1800. How much would he have to sell in a month if he wants to have a monthly income of $2200?
income = .11(s - 1800) + 575, where s is his sales
solve :
.11(s-1800) + 575 = 2200
To find out how much the salesman would have to sell in a month to have a monthly income of $2200, we first need to determine the commission he would earn on top of his base salary.
The commission is calculated based on the portion of sales over $1800. So, let's calculate the commission amount first.
Commission = (Total Sales - $1800) * 11%
Now, let's say the salesman would have to sell X amount in a month to reach a monthly income of $2200. To calculate this, we can set up the following equation:
Base Salary + Commission = $2200
Substituting the values:
$575 + Commission = $2200
So, Commission = $2200 - $575 = $1625
Now, we can substitute the commission in terms of total sales into the initial commission formula:
$1625 = (Total Sales - $1800) * 11%
Dividing both sides by 0.11:
($1625/0.11) = Total Sales - $1800
$14772.73 = Total Sales - $1800
Total Sales = $14772.73 + $1800
Total Sales = $16572.73
Therefore, the salesman would have to sell approximately $16,572.73 in a month to have a monthly income of $2200.
To determine the amount he would have to sell in a month to have a monthly income of $2200, let's break down the calculations:
Step 1: Determine the commission he will receive on the portion of sales over $1800.
The commission is calculated as 11% of the portion of sales over $1800.
Step 2: Calculate the total sales receipts he needs to achieve the target income.
The target income is the sum of the base salary, the commission earned, and the amount of sales over $1800.
Let's perform the calculations step-by-step:
Step 1:
Commission on the portion of sales over $1800 = 11% of (Total Sales - $1800)
Step 2:
Target income = Base Salary + Commission + Sales over $1800
Now let's substitute the given values into the formulas and solve for the target sales:
Commission on the portion of sales over $1800 = 11% of (Total Sales - $1800)
Target income = $2200
Substituting the commission formula into the target income formula:
$2200 = $575 + (11% * (Total Sales - $1800)) + (Total Sales - $1800)
Simplifying the equation:
$2200 = $575 + 0.11(Total Sales - $1800) + (Total Sales - $1800)
$2200 = $575 + 0.11Total Sales - $198 + Total Sales - $1800
Combining like terms:
$2200 = 0.11Total Sales + Total Sales - $1423
$2200 = 1.11Total Sales - $1423
Rearranging the equation:
$2200 + $1423 = 1.11Total Sales
$3623 = 1.11Total Sales
Dividing both sides by 1.11:
Total Sales = $3623 / 1.11
Total Sales ≈ $3268.47
Therefore, the salesman would have to sell approximately $3268.47 in a month to have a monthly income of $2200.