Asurvey of 500 farmers showed that of the farmers, 121 grew only wheat, 113 grew only corn, 90 grew only oats, 199 grew wheat, 60 grew wheat and corn, 57 grew wheat and oats, and 182 grew corn. determine the number of farmers who a) grew at least one of the three. b) grew all three, c) did not grow any of the three, d) grew exactly two of the three

Step-by-step explanation:

Let x represent the number of farmers that grew all three crops.

Let y represent the number of farmers that grew corn and oat.

The Venn diagram representing the scenario is shown in the attached photo.

W represents the subset for wheat

C represents the subset for corn

O represents the subset for oat

199 grew wheat. It means that

121 + 57 - x + x + 60 - x = 199

238 - x = 199

x = 238 - 199

x = 39

182 grew corn. It means that

113 + 60 - x + x + y - x = 182

173 + y - x = 182

y = 182 - 173 + 39

y = 48

a) the number of farmers who grew at least one of the three would be

121 + 113 + 90 + 57 - x + 48 - x + 60 - x + x

= 121 + 113 + 90 + 57 - 39 + 48 - 39 + 60 - 39 + 39 = 411

b) the number of farmers that grew all three would be

x = 39

c) the number of farmers who did not grow any of the three would be

500 - 411 = 89

d) the number of farmers who grew exactly two of the three would be

60 - x + 57 - x + 48 - x

= 60 - 39 + 57 - 39 + 48 - 39

= 21 + 18 + 9

= 48

49%

step-by-step explanation:

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