The universal set contains 54 people. A Venn diagram for sets A and B has the following region count

Question

The universal set contains 54 people. A Venn diagram for sets A and B has the following region counts: A only $2x$, both $x+3$, B only $x+1$, and neither $6$. Form an equation and find $x$.[3] Find $n(A\cup B)$ and the number in exactly one set.[2]

Accepted Answer

(a) $x=11$ (b) $48$ and $34$

Solving an unknown region count

Solving an unknown region count

Solution:

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