Question

9 of the children in Manny's class like to play on the jungle gym and 5 like to play on the monkey bars. 4 children like to play on both the jungle gym and the monkey bars. How many children like to play on the monkey bars but not the jungle gym?

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

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I like to play on the jungle gym
I like to play on the monkey bars

children

Answer 1

To solve this problem, we can use a Venn diagram to organize the information provided.

We have the following details:

- Let **A** be the set of children who like to play on the jungle gym.
- Let **B** be the set of children who like to play on the monkey bars.

From the problem:

- \( |A| = 9 \) (the number of children who like the jungle gym)
- \( |B| = 5 \) (the number of children who like the monkey bars)
- \( |A \cap B| = 4 \) (the number of children who like both)

We want to find the number of children who like to play on the monkey bars but not on the jungle gym, which can be represented as \( |B - A| \).

To calculate \( |B - A| \):

1. First, we find the number of children who like only the monkey bars. This can be calculated by subtracting the number of children who like both from those who like the monkey bars:
\[
|B - A| = |B| - |A \cap B| = 5 - 4 = 1
\]

So, 1 child likes to play on the monkey bars but not on the jungle gym.

### Summary:
- The number of children who like to play on the monkey bars but not the jungle gym is **1**.