A person was asked to make a guess about his own weight. He guessed that it is greater than 70 kg. Given that the weight is a whole number and that three guessed that it more than 74 kg but less than 84 kg. His mother said that it is less than 78 kg. Given that the weight is a whole number and that all three guessed correctly. what is the average (in kg) of the possible weights ?

Options

A. A. 76.5 kg
B. B. 76 kg
C. C. 77 kg
D. D. 75 kg

Answer

To solve the problem step by step, we need to analyze the conditions given about the person's weight:

1. **Understanding the Conditions**:
- The person guessed that his weight is greater than 70 kg.
- Another person guessed that the weight is more than 74 kg but less than 84 kg.
- The mother guessed that the weight is less than 78 kg.
- The weight is a whole number.

2. **Establishing the Range**:
- From the first guess, we know the weight (W) must be greater than 70 kg:
\[ W > 70 \]
- From the second guess, the weight must be more than 74 kg but less than 84 kg:
\[ 74 < W < 84 \]
- From the mother's guess, the weight must be less than 78 kg:
\[ W < 78 \]

3. **Combining the Conditions**:
- Now we combine all the conditions:
- From \( W > 70 \) and \( W < 78 \), we have:
\[ 70 < W < 78 \]
- From \( 74 < W < 84 \), we can narrow it down further:
\[ 74 < W < 78 \]
- Thus, the combined conditions give us:
\[ 74 < W < 78 \]

4. **Identifying Possible Whole Number Weights**:
- The whole numbers that satisfy \( 74 < W < 78 \) are:
- 75 kg
- 76 kg
- 77 kg

5. **Calculating the Average**:
- To find the average of the possible weights (75, 76, and 77):
\[ \text{Average} = \frac{75 + 76 + 77}{3} \]
\[ = \frac{228}{3} = 76 \text{ kg} \]

6. **Final Answer**:
- The average of the possible weights is 76 kg.