There are 9 children in a group. 1childcan play the piano. 3 children can play the violin and flute. 2 children can play the cello, saxophone and recorder. The remaining children can play either 4 or 5 instruments each.If the 9 children play a total of 27 instruments between them, how many children play 5 instruments?

To solve this problem, let's break it down step by step.

1. **Total Instruments Played**:  
   There are 9 children in the group, and they play a total of 27 instruments.

2. **Given Information**:  
   - 1 child can play the piano: \(1\) instrument
   - 3 children can play the violin and flute: \(3 \times 2 = 6\) instruments
   - 2 children can play the cello, saxophone, and recorder: \(2 \times 3 = 6\) instruments

3. **Total Instruments Played So Far**:
   - Sum up the instruments played by the children above:
   \[
   1 + 6 + 6 = 13 \text{ instruments}
   \]
   - Therefore, the remaining \(9 - 6 = 3\) children play a total of:
   \[
   27 - 13 = 14 \text{ instruments}
   \]

4. **Children Playing 4 or 5 Instruments**:
   - Let \(x\) be the number of children who play 5 instruments.
   - Let \(y\) be the number of children who play 4 instruments.

   The equation for the total number of instruments played by these children is:
   \[
   5x + 4y = 14
   \]
   And since these are the remaining 3 children, we also have:
   \[
   x + y = 3
   \]

5. **Solving the System of Equations**:
   - From \(x + y = 3\), we can express \(y\) as:
   \[
   y = 3 - x
   \]
   - Substituting this into the first equation:
   \[
   5x + 4(3 - x) = 14
   \]
   - Expanding and simplifying:
   \[
   5x + 12 - 4x = 14
   \]
   \[
   x + 12 = 14
   \]
   \[
   x = 2
   \]

   So, \(x = 2\) and \(y = 3 - 2 = 1\).

Thus, **2 children play 5 instruments each**.

Would you like more details or have any questions?

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Here are some related questions:

1. What would happen if 2 children could play only 1 instrument each?
2. How many instruments does each child play on average?
3. How many total instruments would be played if each child played 4 instruments?
4. What if another child joined the group playing 3 instruments?
5. How would the total change if one child learned an additional instrument?
6. What happens if the child who plays the piano learns one more instrument?
7. How would the solution change if one child dropped out of the group?
8. What if a new child joined and played the violin and flute?

**Tip**: Always check your work by verifying that your solution satisfies the original problem constraints.

Explore how to solve a problem involving 9 children playing musical instruments. Discover how to determine the number of children playing 5 instruments using arithmetic and equations. Suitable for Grades 6-8.

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