Understanding Percentages in Sales Commissions: Finding the Correct Calculation

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Homework Help Overview

The discussion revolves around understanding the calculation of a salesperson's commission based on a percentage of the selling price of cars. The original poster is confused about how to correctly express the commission for two cars sold at $14,000 each, particularly regarding the interpretation of the variable "k" as a percentage.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the meaning of "k percent" and its implications for calculating commission, questioning whether "k" should be treated as a whole number or a decimal. Some participants discuss the mathematical translation of percentages into fractions and the correct application of these concepts in the problem.

Discussion Status

There is a mix of clarifications regarding the interpretation of "k" as a percentage. Some participants provide guidance on how to approach the calculation, while others emphasize the importance of understanding the reasoning behind the methods rather than just arriving at the correct answer.

Contextual Notes

Participants note that the original poster's confusion stems from the assumption about the nature of "k" and its representation as a percentage. There is an ongoing exploration of how to correctly interpret and apply the concept of percentages in this context.

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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
 
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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.
 
Well, in the problem they stated "k percent", assuming that k is now theoretically a fraction/decimal.
 
Medet said:
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.
 
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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.
 
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Thank you very much. I understand now.
 
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.
 
Harriet said:
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
Harriet said:
(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.
 
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?
 

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