The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is

### Concept & Strategy When a new person joins and raises the average, their weight is equal to the old average plus the total weight increase distributed among all members (including themselves). Make sure all units are consistent (convert grams to kilograms). ### Step-by-Step Solution * **Convert units:** The increase is 400 g. Let's convert this to kg: $$400 \text{ g} = 0.4 \text{ kg}$$ * **Calculate initial total weight:** For 24 students with an average of 35 kg: $$Sum_{initial} = 24 \times 35 = 840 \text{ kg}$$ * **Calculate new total weight:** Including the teacher makes 25 people. The new average is $35 + 0.4 = 35.4 \text{ kg}$: $$Sum_{new} = 25 \times 35.4 = 885 \text{ kg}$$ * **Find the teacher's weight:** $$Teacher = 885 - 840 = 45 \text{ kg}$$ ### Exam Strategy & Shortcut Avoid calculating large multiplications like $24 \times 35$. Use the deviation shortcut. The teacher brings a base weight of 35 kg (the old average), plus enough extra weight to raise the average of all 25 people by 0.4 kg. $$Weight = \text{Old Average} + (\text{Total New Members} \times \text{Increase})$$ $$Weight = 35 + (25 \times 0.4)$$ $$Weight = 35 + 10 = 45 \text{ kg}$$ ### Common Pitfall Forgetting to convert 400 grams into kilograms before calculating. Adding 400 directly to 35 will lead to bizarre and incorrect results. Always normalize your units first. ### Final Answer **Therefore, the correct answer is 45 kg.**