Question

5 of the children in Cora's class like to use markers. 9 children like to use crayons, and 3 children like to use both markers and crayons. How many children like to use markers or crayons or both?

Hint: Copy and complete the Venn diagram below to help you solve the problem.

​
I like to use markers
I like to use crayons

children

Answer 1

To solve the problem, we can use the principle of inclusion-exclusion. We can define the following:

- Let \( M \) be the number of children who like to use markers.
- Let \( C \) be the number of children who like to use crayons.
- Let \( B \) be the number of children who like to use both markers and crayons.

From the information given:
- \( M = 5 \) (children who like markers)
- \( C = 9 \) (children who like crayons)
- \( B = 3 \) (children who like both)

We want to find the total number of children who like markers or crayons (or both). This can be calculated using the formula:

\[
\text{Total} = M + C - B
\]

Substituting the values we have:

\[
\text{Total} = 5 + 9 - 3 = 11
\]

Thus, the number of children who like to use markers or crayons or both is **11**.

### Venn Diagram Representation

To visualize it in a Venn diagram:

1. **In the "Markers" circle**: There are 5 children who like markers.
- Out of the 5, 3 children also like crayons. So the number of children who only like markers: \( 5 - 3 = 2 \).

2. **In the "Crayons" circle**: There are 9 children who like crayons.
- Out of the 9, 3 children also like markers. So the number of children who only like crayons: \( 9 - 3 = 6 \).

Therefore, the count in each section of the Venn diagram will be:
- Only markers: \( 2 \)
- Only crayons: \( 6 \)
- Both markers and crayons: \( 3 \)

And the total number of children represented in the Venn diagram gives us \( 2 + 6 + 3 = 11 \).