SOLUTION: 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 surv

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?
Found 3 solutions by Boreal, ikleyn, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
p(A or B)=p(A)+p(B)-p(A and B)
rather than use probability here, just use the numerator
There are 45 survivors.
45=30+37-both
both=22 of them
Answer by ikleyn(52896)   (Show Source): You can put this solution on YOUR website!
.
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.

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. ANSWER. The number of those survivors who perform both tasks is 19.

Solved.

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

Comment from student :   n(H∆G)=n(H)+n(G)-2[∩(H∩G)]   ∩(H∩G)=[n(H)+n(G)-n(H∆G)]/2

My response :   Probably, you were going to write

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

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

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

So, I know everything of it . . .

Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
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?

19 is correct.
With that, 45 - 19, or 26 grow broccoli ONLY. In addition, 30 - 19, or 11 hunt ONLY.
Therefore, 37 (26 + 11), or Broccoli-growing ONLY and hunting ONLY, respectively, perform ONLY 1 of the 2 tasks (GIVEN).
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