Write A Linear Equation for Monthly Salary + Commission

In summary, the linear equation for the monthly wage W in terms of monthly sales S for a pharmaceutical salesperson who receives a monthly salary of $5000 plus a commission of 7% of sales is W(S) = 0.07(S) + 5000. You should also practice checking your results and seeking help when needed. The study of mathematics allows for solutions to be verified without the approval of experts.
  • #1
nycmathguy
Homework Statement
Write a linear equation.
Relevant Equations
y = mx + b
Write a linear equation for the application.

A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson’s monthly wage W in terms of monthly sales S.

Solution:

I am looking for W(S).

S = monthly sales

Let 7% become 0.07.

I say the linear equation is
W(S) = 0.07(S) + 5000.

You say?
 
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  • #2
I agree.
 
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  • #3
You should also practice checking your results. That is a very, very important skill. If your answer matches every statement of the problem, then it is valid.
You should start to show some work to check and ask for help if you get stuck.
 
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  • #4
FactChecker said:
You should also practice checking your results. That is a very, very important skill. If your answer matches every statement of the problem, then it is valid.
You should start to show some work to check and ask for help if you get stuck.
Strongly agree...
 
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  • #6
FactChecker said:
You should also practice checking your results.
One feature of the study of mathematics that I appreciated was that, for many types of problems, you don't need the approval of experts to verify that you are on the right track. Pretty much any type of problem in which a solution is called for can be checked to verify that solution, all the way from the simplest linear equations (as in this problem) up to the solutions of systems of differential equations.
 
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  • #7
Thank you everyone.
 

1. What is a linear equation?

A linear equation is an algebraic equation that represents a straight line when graphed. It is written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

2. How do you write a linear equation for monthly salary + commission?

To write a linear equation for monthly salary + commission, you would first need to identify the variables involved. Let x represent the monthly salary and y represent the commission. The linear equation would then be y = mx + b, where m is the commission rate and b is the base salary. The equation can be written as y = 0.10x + 2000, for example, if the commission rate is 10% and the base salary is $2000.

3. How do you calculate the commission rate?

The commission rate is calculated by dividing the commission amount by the total sales. For example, if the commission is $500 and the total sales are $5000, the commission rate would be 500/5000 = 0.10 or 10%.

4. Can a linear equation for monthly salary + commission be used for any job?

Yes, a linear equation can be used for any job that involves a monthly salary and commission. The specific values for the slope and y-intercept may vary depending on the job and commission structure, but the general form of y = mx + b can be applied.

5. How can a linear equation for monthly salary + commission be useful?

A linear equation for monthly salary + commission can be useful for predicting and planning for future earnings. By plugging in different values for x (monthly salary), you can see how the commission (y) would change. This can help with setting goals, budgeting, and making financial decisions.

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