Understanding Percentages in Sales Commissions: Finding the Correct Calculation

[Medet]

Homework Statement

A salesperson's commission is k percent of the selling price of a car. Which of the following represents the commission, in dollars, on 2 cars that sold for 14,000 each?

Homework Equations

28,000*k (I thought that this answer was corrects since a percent is always part of 1. For example, .98 would be 98%)

The correct answer is actually 280*k. I'm assuming now that the percent is a whole number and not actually a percent and that they re-arranged the idea of percent by dividing the price of the two cars by a 100.So, I'm just really confused and if anyone can help out that would be awesome.

-MW

 

[Simon Bridge]

Welcome to PF;
The "k" is the percentage - but a percentage is not a fraction, it the number of parts out of 100.
In the notation "10%", the percentage is "10". The "%" sign contains the "divide by 100" part to turn it into a fraction.

It does not have to be a whole number. You can have 0.5% of something for example.

the sentence "k percent of 5000" (for example) means (k/100)x5000 = 50k
this is because "per" means "divide by", "cent" means "100" and "of" means "multiply by"
... you just translate the english sentence into maths.

 

[Medet]

Well, in the problem they stated "k percent", assuming that k is now theoretically a fraction/decimal.

 

[.Scott]

Well, in the problem they stated "k percent", assuming that k is now theoretically a fraction/decimal.

If k=100, "k percent" would be 100%.
If he received 100% of the 28000, that would be 280k.

If k=50, "k percent" would be 50%.
If he received 50% of the 28000, that would be 14000 or 280k.

If k=14.285714..., k percent would 14.285714...%
If he received 14.285714...% of the 14000, that would be 2000 or 280k.

They are expressing k as a percent value with a normal range of 0 to 100. Not a simple multiplier with a normal range of 0 to 1.

 

[Simon Bridge]

Well, in the problem they stated "k percent", assuming that k is now theoretically a fraction/decimal.

... that was an incorrect assumption.
That is not what "k percent" means.

Scott and I are telling you the correct meaning so that next time you see that statement or one similar to it you will know what to do.

 

[Medet]

Thank you very much. I understand now.

 

[Harriet]

I have a question: Could you also do it this way?

Since k is a one digit number, move the decimal point over two places to get .0k (like you would if you were making a one digit number into a percent). Move the decimal in 28,000 over two places also to get 280.

 

[Mark44]

I have a question: Could you also do it this way?

Since k is a one digit number, move the decimal point over two places to get .0k

It's better to write it as (.01)k

(like you would if you were making a one digit number into a percent). Move the decimal in 28,000 over two places also to get 280.

 

[Simon Bridge]

In post #1 you are told that k is already a percentage, you are not told that it is a 1 digit number.
Getting the same amswer as the model answer is not the point. The point is to learn good reasoning skills. What is the reasoning that leads you to attempt that method?