in a class of 50, 30 offer economics,17 offer government and 7 offer neither of the two subjects. how many students offer both subjects
30 + 17 - b + 7 = 50
Student
To find the number of students who offer both subjects, we can use the principle of inclusion-exclusion. This principle states that if we want to calculate the number of elements in the union of two sets, we need to consider the number of elements in each set and subtract the number of elements in their intersection.
Let's denote the number of students who offer both subjects as x. We are given the following information:
- Total number of students in the class: 50
- Number of students who offer economics: 30
- Number of students who offer government: 17
- Number of students who offer neither of the two subjects: 7
We can now set up equations using this information:
Number of students who offer economics = Number of students who offer both subjects + Number of students who offer economics only + Number of students who offer neither of the two subjects
30 = x + (students who offer economics only) + 7
Number of students who offer government = Number of students who offer both subjects + Number of students who offer government only + Number of students who offer neither of the two subjects
17 = x + (students who offer government only) + 7
We can simplify the equations:
x + (students who offer economics only) = 23
x + (students who offer government only) = 10
Now we can subtract the second equation from the first to eliminate the x term:
(x + (students who offer economics only)) - (x + (students who offer government only)) = 23 - 10
(students who offer economics only) - (students who offer government only) = 13
Since we don't know the individual number of students who offer economics only or government only, we cannot determine the exact value of x (students who offer both subjects). We can only say that there are at least 13 students who offer both subjects based on the given information.