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Question

Two hundred eighty-eight teachers were surveyed regarding their plans for the upcoming weekend. The results were as follows:

139	plan to grade papers
139	plan to attend a football game
132	plan to do household chores
30	plan to grade papers and attend a football game
71	plan to grade papers and do household chores
48	plan to attend a football game and do household chores
11	plan to grade papers, attend a football game, and do household chores

Sketch a Venn diagram and answer the questions below.  

1. How many planned to only grade papers?

1. How many planned to grade papers or do household chores?

1. How many did not plan to do any of these activities?

1. How many planned to do at lease two of these activities?
2. How many planned to attend a football game and do household chores, but did not have any plans to grade?

How many planned to attend a football game or grade papers, but did not plan to do household chores؟

1. How many planned to do at most one of these activities?

Answer 1

[1] A+B+C+D+E+F+G+H = 288

[2] A+B+D+E = 139

[3] B+C+D+F = 139

[4] D+E+F+G = 132

[5] B+D = 30

[6] D+E = 71

[7] D+F = 48

[8] D = 11

With problems like this, you usually work from the last information backwards.

[8] D = 11

[8] and [7] F = 37 [9]

[8] and [6] E = 60 [10]

[5] and [8] B = 19 [11]

[4] and [8] and [10] and [9] G = 24 [12]

[3] and [11] and [8] and [9] C = 72 [13]

[2] and [11] and [8] and [10] A = 60 [14]

[1] and [14] and [11] and [13] and [8] and [10] and [9] and [12] H = 5 [15]

How many planned to only grade papers? A = 60

How many planned to grade papers or do household chores?

A+B+D+E+F+G = 211

How many did not plan to do any of these activities? H = 5

How many planned to do at least two of these activities? B+D+E+F = 127

How many planned to attend a football game and do household chores,

but did not have any plans to grade? F=37

How many planned to attend a football game or grade papers,

but did not plan to do household chores? C+F+G = 133

How many planned to do at most one of these activities? A+C+G+H = 161