Answer:
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
