In a class of 50 students, the number of students who offer Accounting is twice as the number who offer Economics. 10 students offer neither of the two subjects and 5 students offer both subjects.
How many students offer Accounting?
How many students offer Economics?
How many students offer only one subjects?
Let's denote the number of students who offer Accounting as A and the number of students who offer Economics as E.
We know that A = 2E (since the number of students who offer Accounting is twice the number who offer Economics).
We also know that 10 students offer neither subject and 5 students offer both subjects.
Let's solve these equations simultaneously:
A + E + 5 = 50 (since the total number of students is 50)
A + E + 5 + 10 = 50 (since 10 students offer neither subject)
A + E + 15 = 50
A + E = 50 - 15
A + E = 35
Now we have two equations:
A = 2E
A + E = 35
Substituting the value of A from the first equation into the second equation, we get:
2E + E = 35
3E = 35
E = 35/3
E ≈ 11.67
Since we can't have a fraction of a student, we round down E to 11.
Therefore, the number of students who offer Economics is 11.
Substituting the value of E into the equation A = 2E, we get:
A = 2(11)
A = 22
Therefore, the number of students who offer Accounting is 22.
To find the number of students who offer only one subject, we subtract the number of students who offer both subjects from the total number of students who offer Accounting and Economics:
Number of students who offer only one subject = (A + E) - 5
Number of students who offer only one subject = (22 + 11) - 5
Number of students who offer only one subject = 33 - 5
Number of students who offer only one subject = 28
Therefore, 28 students offer only one subject.