SOLUTION: How do I solve this sum In a class, 64% of the students take economics and 56% take accounting. How many students take both subjects?

Question 996798: How do I solve this sum
In a class, 64% of the students take economics and 56% take accounting. How many students take both subjects?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(a or b) = a + b - (a and b)

if 64% take economics and 56% take accounting, then 20% must take both.

let's assume 100 students.

64 take economics and 56 take accounting.

that's a total of 64 + 56 = 120

since there are only 100 students, 20 must take both.

now we look at the 64 that take economics and strip out the ones who take both.

we get 44 take economics only and 20 take take both.

now we look at the 56 who take accounting and strip out the ones who take both.

we get 36 who take accounting only and 20 who take both.

we are left with:

44 who take economics only.
36 who take accounting only.
20 who take both.

total is 44 + 36 + 20 = 100.

the ones who take both were being double counted.

they were counted once in the group that takes economics and they were counted once in the group that takes accounting, resulting in the double counting.

you had under economics, 44 took it only and 20 also took accounting.
you had under accounting, 36 took it only and 20 also took economics.

the 20 who took economics and accounting are the same 20 who took accounting and economics.

take one of those set of 20 away and the count becomes accurate.

that's why (A or B) = A + B - (A and B)

(economics or accounting) = economics + accounting - (economics and accounting).

Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
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See also the lesson Counting elements in sub-sets of a given finite set in this site, where the solutions of similar problems are presented.

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