Algebra Assignment: Linear Equations for Salary Calculations Problem

This assignment addresses a real-world problem using linear equations. The scenario involves Inept Industries, where the student is tasked with calculating employee salaries across three levels based on provided starting salaries and salary increases over a three-year period. The solution involves formulating linear equations for each employee level (Level 1, Level 2, and Level 3) using the given data. These equations are then used to determine the number of years it takes for employees to reach specific salary levels, such as promotion to the next level. The solution provides step-by-step calculations, demonstrating the application of slope and linear equations to solve the salary-related problems. References to mathematical concepts and resources support the approach, offering a clear and practical application of algebra in a business context. The student utilizes the information provided to create equations which help determine the number of years for promotion.

Running head: Algebra
Algebra
Name of the University
Name of the Student

2Algebra

3Algebra
Dear Ima Bumbler,
The predicament you are in is regrettable and can be worked out with a little help from
standard mathematical techniques. As it was mentioned that the models follows a linear
pattern so the questions you want answered have been done keeping that in mind.
Here’s a proposed method for finding out what you want.
There are three levels of employees; level 1, level 2 and level 3. It was given that the growth
of salary over time had a linear relation.
Therefore
rate of increase in salary for level 1: (19000−15000)
3 = 4000
3 =$ 1333.33 per year
rate of increase in salary for level 2 : (36000−30000)
3 = 6000
3 =$ 2000 per year
rate of increase in salary for level 3: (58000−50000)
3 = 8000
3 =$ 2666.67 per year
The salary of individuals can be known by forming a linear equation with salary and number
of years as variables. However the equations will vary according to the level of the employee:
If y represents the salary of an employee and x the number of years.
Then for
Level 1 employee: y=1333.33 x +15000, for the first 3 years
Level 2 employee: y=2000 x +30000, for the first 3 years
Level 3 employee: ¿ 2667.67 x+50000 , for the first 3 years.
Thus knowing the level of the employee and number of years they have been working for the
salary of the employee can be found out by using the above three equations.

4Algebra
Level 1 employees can be expected to be promoted to level 2 when their salary increases to
30000. From the linear model developed putting y = 30000, we have:
30000=1333.33∗x +15000
15000=1333.33∗x
⟹ x= 15000
1333.33 ⇒ 11.24 years=12 years(¿)
Similarly the number of years level 2 employees would take to be promoted to level 3 can be
found by plugging in $50000 in the linear model for level 2 employees:
50000=2000 x +30000
⟹ x=10 years.
Thus, it is clear that the level 1 employees will take around 12 years to be promoted to level 2
and level 2 employees will take around 10 years to be promoted to level 3.
Hoping this was helpful.
Yours Sincerely,
Maths Department.

5Algebra
References:
Bednarz, N., Radford, L., Janvier, B. and Lepage, A., 2014. ARITHMETICAL AND
ALGEBRAIC THINKING lN PROBLEM-SOLVING.
Cockcroft, W.H., 1982. Mathematics counts. London: HM Stationery Office.