Solve the problem.
A salesperson gets a commission of $600 for the first $10,000 of sales, and then $300 for each additional $10,000 or partial of sales. Let S(x) represent the commission on x dollars of sales. Find the value of S(45,000)
Well, let's break down the problem and have some fun with it!
First, we know that the salesperson gets $600 for the first $10,000 of sales. That's some nice commission right there! But what happens after that?
For each additional $10,000 or partial of sales, the salesperson gets $300. So, to find the commission on $45,000 of sales, we need to figure out how many additional $10,000 or partials are there.
We have $10,000 in the first bracket and then $35,000 remaining. If we divide this amount by $10,000, we get 3 and a half brackets. But, alas, we can't have half a bracket, so we'll round it down to 3 brackets.
So, for the additional $30,000 (3 brackets of $10,000 each), we have a commission of 3 brackets * $300 per bracket = $900.
Now, let's add this to the initial $600 commission. $900 + $600 = $1500.
So, the value of S(45,000) is $1500.
Hope that answered your question with a smile! If you need anything else, feel free to ask!
To find the value of S(45,000), we need to determine the total commission earned for $45,000 of sales.
First, we calculate the commission for the first $10,000 of sales, which is $600.
Then, we find the commission for the remaining $35,000 of sales by dividing it into units of $10,000.
$35,000 ÷ $10,000 = 3.5
Since the sales were done in increments of $10,000, we can only calculate the commission up to the nearest whole unit. Therefore, we consider 3 units of $10,000, which totals $30,000.
For the additional $5,000, we calculate the commission using the rate of $300 for each $10,000 or partial of sales.
For $5,000, the commission is:
$5,000 ÷ $10,000 = 0.5
0.5 × $300 = $150
So, the commission for the additional $5,000 is $150.
Now, we can calculate the total commission:
$600 (first $10,000) + $30,000 (3 units of $10,000) + $150 (additional $5,000) = $6300
Therefore, the value of S(45,000) is $6,300.
To find the value of S(45,000), we need to determine the commission for $45,000 of sales using the given information about the commission structure.
The commission is $600 for the initial $10,000 of sales, and then $300 for each additional $10,000 or partial thereof. This means that for each additional $10,000 of sales beyond the initial $10,000, the commission increases by $300.
To find the commission for $45,000 of sales, we need to determine how many additional $10,000 increments are included in this amount.
Since $45,000 is $35,000 more than the initial $10,000, we divide $35,000 by $10,000 to find out how many additional increments of $10,000 are included.
35,000 ÷ 10,000 = 3.5
This means that the $45,000 of sales includes 3 additional increments of $10,000.
For the initial $10,000 of sales, the commission is $600.
For the 3 additional increments of $10,000, the commission increases by $300 each time. So, the additional commission for each increment is $300 * 3 = $900.
To find the total commission for $45,000 of sales, we add the commission for the initial $10,000 to the additional commission for the 3 increments of $10,000:
$600 + $900 = $1500
Therefore, the value of S(45,000) is $1500.