A survey of 80 farmers found that 50 grow maize and 60 grow rice. If x of them grow both crops, write an equation in x and solve for it.

Let $x$ be the number of farmers who grow both maize and rice, i.e., $|M \cap R| = x$.
Using the Principle of Inclusion-Exclusion:

$$|M \cup R| = |M| + |R| - |M \cap R|$$ $$80 = 50 + 60 - x$$ $$80 = 110 - x$$ $$x = 110 - 80$$ $$x = 30$$

So, 30 farmers grow both crops.

Number of farmers who grow only maize: $|M| - x = 50 - 30 = 20$.
Number of farmers who grow only rice: $|R| - x = 60 - 30 = 30$.

A Venn diagram would show two overlapping circles.

• The intersection (farmers growing both maize and rice) contains 30 farmers.
• The part of the maize circle outside the intersection (farmers growing only maize) contains 20 farmers.
• The part of the rice circle outside the intersection (farmers growing only rice) contains 30 farmers. The sum of these parts is $20 + 30 + 30 = 80$, which is the total number of farmers.

Find the number of farmers who grow

This is the number of farmers in set $R$ but not in set $M$.

$$|R \text{ only}| = |R| - |M \cap R|$$ $$|R \text{ only}| = 60 - 30$$ $$|R \text{ only}| = 30$$

The number of farmers who grow only rice is $\boxed{30}$.

This is the number of farmers in set $M$ but not in set $R$.

$$|M \text{ only}| = |M| - |M \cap R|$$ $$|M \text{ only}| = 50 - 30$$ $$|M \text{ only}| = 20$$

The number of farmers who grow only maize is $\boxed{20}$.

This refers to the total number of farmers who grow at least one of the crops, which is given as the total number of farmers in the village.

$$|M \cup R| = 80$$

The number of farmers who grow either rice or maize is $\boxed{80}$.