In a class of 50 students the number of number who offer accounting is twice as the number who offer economics .10 students offer neither of the two subjects. 1.illustrate the information on a Venn diagram.2.how many students offer accounting?3.how many students offer economics?4.how many students offer only one subject.
To answer your questions and illustrate the information on a Venn diagram:
1. Creating a Venn diagram:
a. Draw a circle and label it "Accounting."
b. Draw another circle that overlaps with the first circle and label it "Economics."
c. Write "Neither" outside the circles.
d. Include a label for the total number of students, which is 50.
Now let's move on to answering your questions:
2. How many students offer accounting?
Since the number of students who offer accounting is twice the number who offer economics, let's represent the number of students who offer economics as "x." This means the number of students who offer accounting would be 2x.
So, accounting = 2x.
3. How many students offer economics?
As mentioned above, the number of students who offer economics is represented by "x."
4. How many students offer only one subject?
To find the number of students who offer only one subject, we need to subtract the number of students who offer both accounting and economics from the total number of students offering each subject individually.
Since we know that accounting = 2x and economics = x, the number of students who offer both subjects can be represented as x.
The number of students offering only accounting (accounting only) is 2x - x = x.
The number of students offering only economics (economics only) is x - x = 0.
However, we are given that 10 students offer neither subject, so we must subtract this from the total number of students to get the number of students offering only one subject.
Total students = accounting only + economics only + both subjects + neither
Using the information given, the equation becomes:
50 = x + 0 + x + 10
Simplifying the equation, we get:
50 = 2x + 10
Now, we can solve for x:
Subtracting 10 from both sides, we have:
40 = 2x
Dividing both sides by 2, we find:
x = 20
Therefore:
- The number of students who offer accounting = 2x = 2 * 20 = 40 students.
- The number of students who offer economics = x = 20 students.
- The number of students who offer only one subject = accounting only + economics only = 40 + 0 = 40 students.