What is her rate of commission for the sales over $25,000?

Question

Marie Stefanski sells outdoor grills. She knows she earns 10% commission on the first $10,000 and 12% on the next $15,000. She does not remember the rate on the sales of more than $25,000. Her total sales for the month are $30,000 and her total commission is $3,550. What is her rate of commission for the sales over $25,000?

Answer 1

Hello Moni,

Here is the solution to the problem:

 

Let us suppose the rate of commission for sale over $25,000 = x%

 

Now, the total sales amount given = $30,000

 

The following table shows the sales amount, remaining amount, and the commission:

 

Sales Amount (in $)      Remaining Amount (in $)                 Commission on sales amount (in $)

10,000                            30,000 - 10,000 = 20,000                     10% * 10,000 = 1,000

15,000                            20,000 - 15,000 = 5,000                       12% * 5,000 = 1,800

5,000                               5,000 - 5,000 = 0                                x% * 5,000 = 50x

Total = 30,000                                                                         Total = 2,800 + 50x

 

As per the question, since the total commission = $3,550,

We have the following equation:

2,800 + 50x = 3,550

50x = 750

x = 15

 

Hence the rate of commission for the sales over $25,000 = 15%

Answer 2

Hi Moni, let x represent the unknown percent (as a decimal). Then the solution is:

 

.10 * 10000 + .12 * 15000 + x * 5000 (amount over 25000) = 3550

 

1000 + 1800 + x * 5000 = 3550

 

2800 + x * 5000 = 3550

 

Subtract 2800 from both sides of the equation giving:

 

x * 5000 = 750

 

Divide both sides of the equation by 5000 giving:

 

x = 750 / 5000 = 3/20, which is .15 and as a percentage, 15%

 

Questions?