In a class of 50 students, the number of students who study accounting is twice the number of students who study economics and 5 students study both subject while 10 students do not study neither of the two subject. find
A.students who study accounting.
B.illustrate on a Venn diagram
C.students who study economics.
A. 25 students who study accounting
B.
Accounting ___________ Economics
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5
C. 20 students who study economics
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To solve this problem, we can use a Venn diagram to visually represent the given information. A Venn diagram uses overlapping circles to show relationships between different sets of items or elements.
Let's define our sets:
A = Students who study accounting.
B = Students who study economics.
C = Students who study both subjects.
Given information:
- The number of students who study accounting is twice the number of students who study economics.
- 5 students study both subjects.
- 10 students do not study either subject.
Now let's proceed step by step to find the answers:
Step 1: Calculate the number of students who study both subjects.
From the given information, we know that 5 students study both accounting and economics (C = 5).
Step 2: Calculate the number of students who only study accounting.
Since the number of students who study accounting is twice the number of students who study economics, we can use this relationship to find the number of accounting-only students. Let's assume the number of students who study economics is X. Therefore, the number of students who study accounting would be 2X. Since C represents the number of students who study both subjects, the total number of accounting students would be 2X - C.
Step 3: Calculate the number of students who only study economics.
Similar to Step 2, the number of students who only study economics would be X - C.
Step 4: Calculate the total number of students who study either subject.
To find the total number of accounting students, we can add the students who study both subjects (C) and the students who only study accounting from Step 2. So, the total number of accounting students is C + (2X - C), which simplifies to 2X.
Similarly, the total number of economics students would be C + (X - C), which simplifies to X.
Step 5: Find the value of X.
To find the value of X, we need to use the information that 10 students do not study either subject. This means that the total number of students who study either subject is 50 - 10 = 40.
Therefore, we can set up an equation using the information from Step 4 and Step 5:
2X + X = 40
3X = 40
X = 40/3
Step 6: Calculate the final values.
Now that we have the value of X, we can substitute it back into our equations from Step 2 and Step 3 to find the final values.
A = 2X - C = 2(40/3) - 5 = 80/3 - 5
B = X - C = (40/3) - 5
Calculating the final values, we'll get:
A = 65/3
B = 25/3
So, the answers are:
A. The number of students who study accounting = 65/3
B. The Venn diagram will have two overlapping circles representing accounting and economics, with 5 students in the overlapping region.
C. The number of students who study economics = 25/3