The average weight of 38 children in a class is $15 ext{ kg}$. If 4 children leave the class, each having an average weight of $40 ext{ kg}$, and then 2 new children join the class with an average weight of $35 ext{ kg}$, what is the new average weight of all the children in the class?

Question

The average weight of 38 children in a class is $15 	ext{ kg}$. If 4 children leave the class, each having an average weight of $40 	ext{ kg}$, and then 2 new children join the class with an average weight of $35 	ext{ kg}$, what is the new average weight of all the children in the class?

Accepted Answer

**Solution:**

1. Calculate the total weight of all 38 children initially:
   - Total weight = Average weight × Number of children = $15 	imes 38 = 570 	ext{ kg}$

2. Calculate the total weight of the 4 children who left:
   - Total weight of 4 children = $40 	imes 4 = 160 	ext{ kg}$

3. Calculate the total weight of the 2 children who joined:
   - Total weight of 2 children = $35 	imes 2 = 70 	ext{ kg}$

4. Find the new total number of children:
   - New number = $38 - 4 + 2 = 36$

5. Calculate the new total weight:
   - New total weight = Initial total weight - Weight of children who left + Weight of children who joined
   - New total weight = $570 - 160 + 70 = 480 	ext{ kg}$

6. Calculate the new average weight:
   $$	ext{New average} = \frac{	ext{New total weight}}{	ext{New number of children}} = \frac{480}{36} = \frac{40}{3} 	ext{ kg}$$

**Answer:** $\frac{40}{3} 	ext{ kg}$

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