In a class of 50 student's, the number of student's who offer Accounting is twice as the number who offer Economics. 10 students offer neither of the two subject, 5 students offer both subject.
(1) how many students offer Accounting.
(2)how many students offer Economics.
How many students offer only one subject.
AAAaannndd the bot gets it wrong yet again!
as before, if x do econ, then
x + 2x - 5 = 50-10
x=15
so
econ: 15
accounting: 30
econ only: 15-5 = 10
accounting only: 30-5 = 25
so 35 do only one subject
To find the number of students who offer Accounting, we'll start by denoting the number of students who offer Accounting as "A" and the number of students who offer Economics as "E."
From the given information, we know that A = 2E, as the number of students who offer Accounting is twice the number who offer Economics.
We'll now use this information to create a Venn diagram.
Let's fill in the diagram step by step:
Total number of students = 50
Students who offer neither subject = 10
Students who offer both subjects = 5
1) Accounting only: A - (A ∩ E)
We know A = 2E, so substituting this value gives:
Accounting only = 2E - 5
2) Economics only: E - (A ∩ E)
Economics only = E - 5
3) Accounting only + Economics only + Both subjects + Neither subject = Total number of students:
(2E - 5) + (E - 5) + 5 + 10 = 50
Simplifying the equation:
2E - 5 + E - 5 + 5 + 10 = 50
3E + 5 = 50
3E = 45
E = 15
Now we can find the answers to the questions:
(1) Number of students who offer Accounting:
A = 2E = 2(15) = 30
(2) Number of students who offer Economics:
E = 15
To find the number of students who offer only one subject, we can revisit the calculations for Accounting only and Economics only:
Accounting only = 2E - 5
= 2(15) - 5
= 30 - 5
= 25
Economics only = E - 5
= 15 - 5
= 10
Therefore, the number of students who offer only one subject is 25 + 10 = 35.
To solve this problem, we can use a method called the Inclusion-Exclusion Principle.
Step 1: Draw a Venn diagram to represent the two subjects, Accounting and Economics. Label the areas as A (Accounting), E (Economics), and N (Neither). Also, mark the overlapping area as AE (Both subjects).
Given information:
- Total number of students in the class = 50
- Number of students offering both subjects (AE) = 5
- Number of students offering neither subject (N) = 10
Step 2: Let x represent the number of students offering Accounting. Since the number of students offering Accounting is twice as much as the number offering Economics, the number of students offering Economics will be x/2.
Step 3: Use the formula:
Total = A + E + N - AE
Plugging in the values:
50 = x + x/2 + 10 - 5
Step 4: Simplify the equation:
50 = 1.5x + 5
Subtracting 5 from both sides, we get:
45 = 1.5x
Now, divide both sides by 1.5 to solve for x:
x = 30
Therefore, the number of students offering Accounting (A) is 30, and the number offering Economics (E) is 30/2 = 15.
To find the number of students offering only one subject, we need to subtract the number of students offering both subjects from the total number of students offering each subject.
Number of students offering only Accounting = Number of students offering Accounting - Number of students offering both subjects
= 30 - 5 = 25
Number of students offering only Economics = Number of students offering Economics - Number of students offering both subjects
= 15 - 5 = 10
Therefore, 25 students offer only Accounting, and 10 students offer only Economics.
(1) 25 students offer Accounting.
(2) 15 students offer Economics.
How many students offer only one subject: 30 students offer only one subject.