The average weight of the students in a class is $45 ext{ kg}$. Due to a mistake, the weight of one student was recorded as $84 ext{ kg}$ instead of $48 ext{ kg}$. This error caused the average weight to increase by $0.9 ext{ kg}$. Find the total number of students in the class.

Question

The average weight of the students in a class is $45 	ext{ kg}$. Due to a mistake, the weight of one student was recorded as $84 	ext{ kg}$ instead of $48 	ext{ kg}$. This error caused the average weight to increase by $0.9 	ext{ kg}$. Find the total number of students in the class.

Accepted Answer

**Solution:**

1. Let the total number of students be *n*.

2. The original average weight is $45 	ext{ kg}$, so the total weight of all students is $45n$.

3. Due to the mistake, one student's weight was recorded as $84 	ext{ kg}$ instead of $48 	ext{ kg}$, which means the total weight was increased by:
   
   $$84 - 48 = 36 	ext{ kg}$$

4. This error caused the average to increase by $0.9 	ext{ kg}$, so the new average is:

$$45 + 0.9 = 45.9 	ext{ kg}$$

5. The total weight with the error is also equal to the new average times the number of students:

$$45n + 36 = 45.9n$$

6. Rearranging the equation:

$$45n + 36 = 45.9n$$
   $$36 = 45.9n - 45n$$
   $$36 = 0.9n$$

7. Solving for *n*:

$$n = \frac{36}{0.9} = 40$$

**Answer:** $40$

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