Question

A survey of 500 farmers showed that of the​ farmers, 129 grew only​ wheat, 111 grew only​ corn, 89 grew only​ oats, 202 grew​ wheat, 58 grew wheat and​ corn, 52 grew wheat and​ oats, and 177 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.

Answer 1

To determine the number of farmers who grew at least one of the three crops, add the number of farmers who grew each crop individually. Subtract the number of farmers who grew exactly two crops from the total number who grew all three to find those who grew all three. The number of farmers who did not grow any of the three is found by subtracting the number of farmers who grew at least one crop from the total. The number of farmers who grew exactly two of the three can be found by adding the number of farmers who grew exactly two crops. After solving we get answers 329, 219 ,171 , 110.

Step-by-step explanation:

To determine the number of farmers who grew at least one of the three crops, we need to find the total number of farmers who grew each crop individually and the total number of farmers who grew two or more crops. From the given information, we have:

• The number of farmers who grew only wheat (129)
• The number of farmers who grew only corn (111)
• The number of farmers who grew only oats (89)
• The number of farmers who grew wheat and corn (58)
• The number of farmers who grew wheat and oats (52)
• The number of farmers who grew corn (177)

To find the number of farmers who grew at least one of the three, we add the number of farmers who grew each crop individually:

Total = number of farmers who grew only wheat + number of farmers who grew only corn + number of farmers who grew only oats = 129 + 111 + 89 = 329

To determine the number of farmers who grew all three crops, we need to subtract the number of farmers who grew exactly two crops from the total number of farmers who grew all three:

Number of farmers who grew all three = Total - number of farmers who grew wheat and corn - number of farmers who grew wheat and oats = 329 - 58 - 52 = 219

To find the number of farmers who did not grow any of the three crops, we subtract the total number of farmers who grew at least one crop from the total number of farmers:

Number of farmers who did not grow any of the three = 500 - Total = 500 - 329 = 171

To determine the number of farmers who grew exactly two of the three crops, we add the number of farmers who grew exactly two crops:

Number of farmers who grew exactly two of the three = number of farmers who grew wheat and corn + number of farmers who grew wheat and oats = 58 + 52 = 110