SOLUTION: Suppose set A contains 86 ELEMENTS and the total number ELEMENTS in either Set A or Set B is 90. If the Sets A and B have 33 ELEMENTS in common, how many ELEMENTS are contained in

Algebra ->  Test -> SOLUTION: Suppose set A contains 86 ELEMENTS and the total number ELEMENTS in either Set A or Set B is 90. If the Sets A and B have 33 ELEMENTS in common, how many ELEMENTS are contained in       Log On


   

Question 1050706: Suppose set A contains 86 ELEMENTS and the total number ELEMENTS in either Set A or Set B is 90. If the Sets A and B have 33 ELEMENTS in common, how many ELEMENTS are contained in set be? I have 90 is this correct?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i get B = 37.

the formula to use is:

(A or B) = A + B - (A and B).

you are given that (A or B) = 90
you are given that A = 86
you are given that (A and B) = 33

the formula becomes:

90 = 86 + B - 33

simplify to get 90 = B + 53

subtract 53 from both sides of the equation to get:

B = 90 - 53 = 37.

there are 86 elements in A.
there are 37 elements in B.
there are 33 elements that are in both A and B.

there are 86 - 33 = 53 elements that are in A only.
there are 37 - 33 = 4 elements that are in B only.
there are 33 elements that are in both A and B.

the total elements are 53 + 4 + 33 = 90.