Math Problem Statement

A company has 13 employees. They have an average salary of 31567kr. When a new employee joins the average salary increase with 240kr. What is the new employees salary?

Solution

To solve this problem, let's break it down step by step.

Step 1: Calculate the total salary of the 13 employees

The average salary of the 13 employees is 31,567 kr. So, the total salary of all 13 employees can be calculated by multiplying the average salary by the number of employees:

Total salary of 13 employees=31,567kr×13=410,371kr\text{Total salary of 13 employees} = 31,567 \, \text{kr} \times 13 = 410,371 \, \text{kr}

Step 2: Calculate the total salary of the 14 employees after the new hire

After the new employee joins, the average salary increases by 240 kr, making the new average salary:

New average salary=31,567kr+240kr=31,807kr\text{New average salary} = 31,567 \, \text{kr} + 240 \, \text{kr} = 31,807 \, \text{kr}

Now, to find the total salary of all 14 employees, multiply the new average salary by 14:

Total salary of 14 employees=31,807kr×14=445,298kr\text{Total salary of 14 employees} = 31,807 \, \text{kr} \times 14 = 445,298 \, \text{kr}

Step 3: Calculate the salary of the new employee

The salary of the new employee is the difference between the total salary of 14 employees and the total salary of the original 13 employees:

New employee’s salary=445,298kr410,371kr=34,927kr\text{New employee's salary} = 445,298 \, \text{kr} - 410,371 \, \text{kr} = 34,927 \, \text{kr}

Final Answer:

The new employee's salary is 34,927 kr.

Would you like a more detailed explanation or have any further questions on this?

Here are some related questions you might find interesting:

  1. How would the salary change if the average salary increased by 500 kr instead of 240 kr?
  2. What would the new average salary be if 2 new employees were hired instead of 1?
  3. How can we calculate the average salary if we know the total salary and number of employees?
  4. What is the impact on the average salary if the highest and lowest salaries are significantly different?
  5. How do you handle a situation where an employee's salary is negative or zero?

Tip: When working with averages and totals, it’s useful to remember that the total salary is simply the average salary multiplied by the number of employees. This relationship helps you quickly calculate and solve problems involving changes to averages.

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Math Problem Analysis

Mathematical Concepts

Average
Algebra
Salary Calculation

Formulas

Total Salary = Average Salary × Number of Employees
New Average Salary = Old Average Salary + Increase
New Employee's Salary = Total Salary of New Employees - Total Salary of Original Employees

Theorems

Basic Arithmetic and Algebra

Suitable Grade Level

Grades 6-8