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A survey of 500 farmers showed that of the​ farmers, 122 grew only​ wheat, 107 grew only​ corn, 93 grew only​ oats, 196 grew​ wheat, 57 grew wheat and​ corn, 53 grew wheat and​ oats, and 170 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, and ​d) grew exactly two of the three.

User Nata
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a) The number of farmers who grew at least one of the three crops is:798

b) The number of farmers who grew all three crops is: 0

c) The number of farmers who did not grow any of the three crops is:−298

d) The number of farmers who grew at least one of the three crops is 798.

Given the survey of 500 farmers, we can use the given information to determine the number of farmers who:

a) grew at least one of the three crops:

To find the number of farmers who grew at least one of the three crops, we need to add the number of farmers who grew only wheat, only corn, only oats, and those who grew two or three of the crops. Therefore, the number of farmers who grew at least one of the three crops is:

122+107+93+57+53+196+170=798

b) grew all three crops:

From the given information, we can see that no farmer grew all three crops. Therefore, the number of farmers who grew all three crops is:

0

c) did not grow any of the three crops:

To find the number of farmers who did not grow any of the three crops, we need to subtract the number of farmers who grew at least one of the three crops from the total number of farmers. Therefore, the number of farmers who did not grow any of the three crops is:

500−798=−298

Since the result is negative, it means that there is an error in the calculation. The correct answer is that we cannot determine the number of farmers who did not grow any of the three crops from the given information.

d) grew exactly two of the three crops:

To find the number of farmers who grew exactly two of the three crops, we need to add the number of farmers who grew wheat and corn, wheat and oats, and corn and oats. Therefore, the number of farmers who grew exactly two of the three crops is:

57+53+0=110

Therefore, the number of farmers who grew at least one of the three crops is 798, the number of farmers who grew all three crops is 0, the number of farmers who did not grow any of the three crops cannot be determined from the given information, and the number of farmers who grew exactly two of the three crops is 110.

User David Osborne
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