Question 1189185
.
All the survivors who live in a certain a post-apocalyptic settlement 
spend their miserable days hunting mutant buffalo or growing broccoli, and some do both. 
If, in total, 45 survivors grow broccoli, 30 hunt, and 37 of them perform only one of those tasks, 
how many perform both tasks?
~~~~~~~~~~~~~~~~



            I read,  understand,  interpret and treat the problem differently from  @Boreal.


            My solution and my answer are different.



<pre>
Let x be the number of those survivors who perform both tasks.


The total population is  45 + 30 - x.

Of them, 37 perform only one of those tasks;
so, the remaining  (45 + 30 -x) - 37  perform BOTH tasks.


It gives this equation

    (45 + 30 - x) - 37 = x


From this equation

    45 + 30 - 37 = x + x

         38      = 2x

          x      = 38/2 = 19.


<U>ANSWER</U>.  The number of those survivors who perform both tasks is 19.
</pre>

Solved.



===============



<U>Comment from student</U> : &nbsp;&nbsp;n(H∆G)=n(H)+n(G)-2[∩(H∩G)] &nbsp;&nbsp;∩(H∩G)=[n(H)+n(G)-n(H∆G)]/2



<U>My response</U> : &nbsp;&nbsp;Probably, &nbsp;you were going to write


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;n(H∆G)=n(H)+n(G)-2[n(H∩G)];  &nbsp;&nbsp;n(H∩G)=[n(H)+n(G)-n(H∆G)]/2.



You should not worry about my education: &nbsp;&nbsp;I graduated from the &nbsp;University, &nbsp;whose rating in &nbsp;Math 


(at the time when I studied there) &nbsp;was higher than &nbsp;MIT, &nbsp;Harvard, &nbsp;Princeton, &nbsp;Caltech etc.



So, I know everything of it . . .