Question

In a group of 80 trees, 37 have red fruits on them and 52 have green fruits, and each tree has at least one of the two colored fruits. Find out how many trees have both red and green fruits.

Answer 1

To find the number of trees that have both red and green fruits, we can use the principle of inclusion-exclusion. Let's denote:

- \( R \): the number of trees with red fruits
- \( G \): the number of trees with green fruits
- \( N \): the total number of trees
- \( B \): the number of trees with both red and green fruits

From the problem statement, we have the following values:

- \( R = 37 \)
- \( G = 52 \)
- \( N = 80 \)

According to the principle of inclusion-exclusion, the total number of trees can be expressed as:

\[
N = R + G - B
\]

Substituting the known values into this equation:

\[
80 = 37 + 52 - B
\]

Now, we can simplify the right side:

\[
80 = 89 - B
\]

Next, we can solve for \( B \):

\[
B = 89 - 80
\]
\[
B = 9
\]

Thus, the number of trees that have both red and green fruits is \( \boxed{9} \).