In class of 50 student, the number of students who offer accounting is twice as who offer economic.10 students offer neither of the two subject, and 5 students offer both subject. Illustrate the information on a venn diagram

Answer 1

To solve the problem and illustrate the information on a Venn diagram, let's start by organizing the given data.

1. Total number of students: 50
2. Students offering neither accounting nor economics: 10
3. Let \( x \) be the number of students who offer economics.
4. Therefore, the number of students who offer accounting: \( 2x \) (since it is twice the number of students offering economics).
5. Students who offer both subjects: 5

Now, we need to calculate how many students are offering only accounting and only economics.

Setting up the calculations:

1. Students offering only accounting: \[ \text{Only Accounting} = 2x - 5 \]

2. Students offering only economics: \[ \text{Only Economics} = x - 5 \]

3. Total students in accounting and economics (including overlaps): \[ \text{Total in A or E} = \text{Only Accounting} + \text{Only Economics} + \text{Both} \] Substituting in: \[ \text{Total in A or E} = (2x - 5) + (x - 5) + 5 = 3x - 5 \]

4. Total students who offer neither subject: 10

5. Using the total student count: \[ \text{Total students} = \text{Total in A or E} + \text{Neither} \] Thus, \[ 50 = (3x - 5) + 10 \] Simplifying this, \[ 50 = 3x + 5 \ 45 = 3x \ x = 15 \]

Calculating the number of students in each category:

• Number of students offering economics: \( x = 15 \)
• Number of students offering accounting: \( 2x = 30 \)

Now, we can find:

1. Only Accounting: \[ 2x - 5 = 30 - 5 = 25 \]
2. Only Economics: \[ x - 5 = 15 - 5 = 10 \]

Summary of counts:

• Only Accounting: 25
• Only Economics: 10
• Both: 5
• Neither: 10

Venn Diagram illustration:

To draw the Venn Diagram:

1. Draw two overlapping circles. Label one circle "Accounting" and the other "Economics."
2. In the overlapping section, write "5" (students taking both).
3. In the Accounting circle (not overlapping), write "25" (students taking only Accounting).
4. In the Economics circle (not overlapping), write "10" (students taking only Economics).
5. Outside of both circles, write "10" (students taking neither subject).

Visual Representation:

          +-----------------------+
          |        Neither        | 10
          |                       |
          |      +-------+      |
          |      |       |      |
          |      |  5    |      |
          |      |       |      |
          |      |-------|      |
          |     /         \     |
          |    /           \    |
          |   |    25      |   |  10
          |   | Accounting |   | 
          |    \         /    |
          |     \       /     |
          |      +-----+      |
          |       Economics    |
          +-----------------------+

This diagram summarizes the distribution of students in the class based on their subject choices.