Question

Hello, I need some help on a question like the one down below.A survey of 1,175 tourists visiting Orlando was taken. Of those surveyed:251 tourists had visited LEGOLAND294 tourists had visited Universal Studios54 tourists had visited both the Magic Kingdom and LEGOLAND80 tourists had visited both the Magic Kingdom and Universal Studios99 tourists had visited both LEGOLAND and Universal Studios38 tourists had visited all three theme parks72 tourists did not visit any of these theme parksHow many tourists only visited the Magic Kingdom (of these three)?

Answer 1

$\begin{gathered} L=251,\text{ tourist who visited legoland} \\ U=294,\text{ visited universal studios} \\ ML=54,\text{ visited magic kingdom and legoland} \\ MU=80,\text{ visited magic kingdom and universal studios} \\ LU=99,\text{ universal studios and legoland} \\ MLU=38,\text{ all three} \\ D=72,\text{ did not visit any} \\ \text{Find }M,\text{ which is the visitors who only visited magic kingdom} \\ M+L+U+D-ML-MU-LU-MLU=1175, \\ M+251+294+72-54-80-99-38=1175 \\ M+346=1175 \\ M=1175-346 \\ M=829 \\ \text{there are 829 tourist whovisited only magic kingdom} \\ \text{explanation, we subtract variables with two or more visited places to avoid double count} \end{gathered}$