Answer: 26 attendees had none of the three.
Step-by-step explanation:
The Venn diagram illustrating the situation is shown in the attached photo.
C represents the set of statisticians that had Caesar salad.
R represents the set of statisticians that had roast beef.
A represents the set of statisticians that had apple pie for dessert.
x represents the number that had Caesar salad and apple pie for dessert only.
y represents the number that had Caesar salad and roast beef.
z represents the number that had roast beef and apple pie for dessert only.
If 15 had at least two of those three offerings,it means that
x + y + z = 15
Therefore,
35 - (x + y + 2) + 28 - (y + z + 2) + 45 - (x + z + 2) + 2 + none = 100
35 - x - y - 2 + 28 - y - z - 2 + 45 - x - z - 2 + 2 + none = 100
35 + 28 + 45 - x - x - y - y - z - z - 2 - 2 - 2 + 2 + none = 100
108 - 2x - 2y - 2z - 4 + none = 100
108 - 4 - 2(x + y + z) + none = 100
Since x + y + z = 15, then
104 - 2(15) + none = 100
74 + none = 100
none = 100 - 74 = 26
