Ryan S. answered • 11/06/13

Mathematics and Statistics

The hint to draw a Venn diagram is a good one. Since I can't do that here, I will describe my diagram. It is 3 circles that overlap to create 7 regions: Failed math only, failed physics only, failed chemistry only, failed math and chemistry but not physics, failed math and physics but not chemistry, failed physics and chemistry but not math, and failed all three. Let the number that failed all three equal x. We then have the following:

Failed math only = 128 - (31-x) - (54-x) - x = 43 + x

Failed physics only = 87 - (31-x) - (30-x) - x = 26 + x

Failed chemistry only = 134 - (54-x) - (30-x) - x = 50 + x

Failed math and chemistry but not physics = 54 - x

Failed math and physics but not chemistry= 31 - x

Failed physics and chemistry but not math = 30 - x

Failed all three = x

The sum of these expressions is 43 + x + 26 + x + 50 + x + 54 - x + 31 - x + 30 - x + x = 234 + x

This expression must equal 250. So 234 + x = 250. Solving for x gives x = 16

a) 16

b) 128 - 31 = 97

c) 134 - 54 = 80

d) physics only = 26 + 16 = 42

e) math only + chemistry only + math and chemistry but not physics = 43 + x + 50 + x + 54 - x = 163

Ryan S.

11/06/13