Solve for salary given averages of other salaries

• Mindscrape
In summary, the problem is to find the salary of a new manager in a factory where the average weekly salary of 12 workers and 3 managers was $600, but decreased to$580 after one manager whose salary was $720 was replaced. Using the equations$\frac{tw+tm}{15}=600$and$tm=m1+m2+720$, the solution can be found by setting up and solving the equations$tw+m1+m2+720=9000$and$tw+m1+m2+m3=8700$, and then subtracting them to get$m3=420$. Alternatively, a shortcut method can be used by reducing the salary of the manager starting at$720$by$-$300 to Mindscrape My wife is working on problems to study for the GMAT, and asks her fellow math nerd (me) to help on some of them. Originally I had an error and wanted to see if any of you could help me find it, but as I was typing I found it myself! Can I still put this up in case someone stumbles on it and it helps them out? The problem is: The average weekly salary of 12 workers and 3 managers in a factory was$600. A manager whose salary was $720 was replaced with a new manager, then the average salary of the team fell to$580. What is the salary of the new manager?

$$\frac{tw+tm}{15}=600$$
where tw represents total worker salary and tm represents total manager salary. Now the second sentence says
$$tm=m1+m2+720$$
so the first equation is now (having multiplied out the 15 from before) -- also label this eqn1
$$tw+m1+m2+720=9000$$
continuing with info from the second sentence, we get the second equation for the newly decreased average as
$$\frac{tw+m1+m2+m3}{15}=580$$
now simplifying gives -- and labeling this eqn2
$$tw+m1+m2+m3=8700$$
subtract the two equations (eqn1-eqn2)
$$720-m3=300$$
for the grand finale...
$$m3=420$$

Nicely done. Since standardized tests often encourage shortcuts, I'll add a supplemental method which cuts through many of the steps.
In general, if you wanted to affect a change of -$20 in the average of 15 salaries, you have to have a total change of 15(-$20)=-$300 to the sum. This could be done by reducing one salary by$300, or reducing all salaries by $20, or anywhere in between. Since the only thing you are changing is the salary starting at$720, you can apply the -\$300 to that.

1. How do I calculate my salary based on the average of other salaries in my field?

To calculate your salary based on the average of other salaries in your field, you will need to gather data on the average salaries for your specific job title and location. You can find this information through salary surveys, job search websites, or by networking with professionals in your field. Once you have the average salary, you can use it as a benchmark to negotiate your own salary based on your qualifications and experience.

2. Why is it important to consider the average salary when negotiating for a salary?

The average salary for a particular job title and location is an important factor to consider when negotiating for a salary because it gives you a benchmark for what is considered a fair and competitive salary in your field. Knowing the average salary can also help you determine if you are being underpaid or overpaid for your position, and can guide your salary expectations during the negotiation process.

3. Are there any other factors besides the average salary that should be considered when negotiating for a salary?

Yes, there are other factors besides the average salary that should be considered when negotiating for a salary. These factors may include your education, experience, skills, and the current job market. It's important to also consider the specific job responsibilities and benefits offered by the company, as these can also impact your salary negotiations.

4. How can I use the average salary to my advantage during salary negotiations?

You can use the average salary to your advantage during salary negotiations by demonstrating your qualifications and experience in relation to the average salary. If you have more experience or a higher level of education than the average, you can use this to justify a higher salary. Additionally, you can use the average salary as a starting point for your negotiations and aim for a salary slightly above the average to account for your unique skills and contributions.

5. Is the average salary always an accurate representation of what I should be earning?

The average salary is a useful benchmark for salary negotiations, but it may not always accurately represent what you should be earning. Factors such as location, company size, and industry can all impact salaries, so it's important to consider these factors in addition to the average salary. It's also important to remember that your salary is ultimately determined by the negotiations between you and your employer, and may not align exactly with the average salary for your position.