Examkin

Question

Difficulty: EasyLinear Equations in One Variable

A company has a total of 150150 employees assigned to either the Marketing department or the Development department. The number of employees in the Development department is 3030 more than 33 times the number of employees in the Marketing department. How many employees work in the Marketing department?

  1. A
    25
  2. 30Answer
  3. C
    40
  4. D
    45
  5. E
    120

Answer

The number of employees working in the Marketing department is 30.
Letting mm represent the Marketing department employees, the Development department has 3m+303m + 30 employees. Summing both yields m+3m+30=150m + 3m + 30 = 150, which simplifies to 4m+30=1504m + 30 = 150. Subtracting 30 gives 4m=1204m = 120, and dividing by 4 yields m=30m = 30.

Step-by-Step Solution

1
Define variables for each department.
Let mm be the number of employees in Marketing. Then the number of employees in Development is 3m+303m + 30.
Expressing both quantities in terms of a single variable simplifies setting up a linear equation.
2
Set up the linear equation representing total employees.
m+(3m+30)=150m + (3m + 30) = 150
The sum of employees in both departments equals the company total of 150.
3
Combine like terms.
4m+30=1504m + 30 = 150
Adding mm and 3m3m gives 4m4m.
4
Isolate the variable term and solve for mm.
4m=120  ⟹  m=304m = 120 \implies m = 30
Subtract 30 from both sides and then divide by 4.

Key Concept

Linear Equations in One Variable - Word Problem Modeling
Estimated Time:1m 0s
Rate this question

Topics

Linear Equations in One Variable

More questions from this topic