Final answer:
The weights of the new kids in the first, second, and third groups are 35 kilograms, 46 kilograms, and 24 kilograms, respectively.
Step-by-step explanation:
To calculate the weight of the new kid in each group, we can use the concept of averages. If the average weight of the kids remains the same after a new kid joins, it means the new kid's weight is the same as the average. If the average increases or decreases, we need to find the difference in total weight that caused the change.
- First Group: Since the average weight of a kid in the first group remains 35 kilograms after the new kid joins, the new kid also weighs 35 kilograms.
- Second Group: To find the new kid's weight in the second group, where the average weight is now 36 kilograms, we use the formula: New Average = (Sum of Original Weights + Weight of New Kid) / (Original Number of Kids + 1). We know the sum of the original weights is 10 kids × 35 kg = 350 kg. The new average is 36 kg for 11 kids, so the total weight is now 11 × 36 kg = 396 kg. Subtracting the original total from the new total gives us the weight of the new kid: 396 kg - 350 kg = 46 kg.
- Third Group: Similarly, for the third group where the average weight is now 34 kilograms, we have: 10 × 35 kg = 350 kg as the original total weight and 11 × 34 kg = 374 kg as the new total weight. The new kid's weight is 374 kg - 350 kg = 24 kg.
The weights of the new kids in the first, second, and third groups are 35 kilograms, 46 kilograms, and 24 kilograms, respectively.