# Set Theory: In a class of 48 students, 22 offered Physics, 20 offered Agricultural science, 18 offered Literature.

#### Safha

##### New member
In a class of 48 students, 22 offered Physics, 20 offered Agricultural science, 18 offered Literature. 3 students offered both Literature and Agricultural science, 4 students offered both Physics and Agricultural Science. Find the number of students that take all the three subjects, If 5 students take non of the subjects.

#### pka

##### Elite Member
In a class of 48 students, 22 offered Physics, 20 offered Agricultural science, 18 offered Literature. 3 students offered both Literature and Agricultural science, 4 students offered both Physics and Agricultural Science. Find the number of students that take all the three subjects, If 5 students take non of the subjects.

Inside the there are a total of 48 students, so $$\displaystyle j+k+m+x+y+z+w+5=48$$.
Now we are looking for z the number that take all three subjects.
The given tells us that $$\displaystyle j+x+w+z=22$$ because twenty-two take physics.
$$\displaystyle x+w=4$$ because four take both physics & agriculture.
You must proceed to establish all equations necessary to find the value of each variable.

#### pka

##### Elite Member
This is a correction Now we are looking for $$\displaystyle \large \color{red}w$$, the number that take all three subjects.

#### Dr.Peterson

##### Elite Member
I see 6 equations for 7 variables. I don't see that we can solve for w. I may be missing something. But is it possible something was omitted from the problem?

#### pka

##### Elite Member
I see 6 equations for 7 variables. I don't see that we can solve for w. I may be missing something. But is it possible something was omitted from the problem?
Well I admit I make a stupid mistake in subtraction. Now I see that some bit of information is missing.
If only I knew how many students take only Agricultural science then there is a unique solution.