The average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new persons?

Answer

To solve the problem step by step, we will use the concept of averages.

### Step 1: Understand the initial average weight
Let the initial average weight of the 8 persons be \( A \) kg. Therefore, the total weight of these 8 persons can be expressed as:
\[ \text{Total weight} = 8A \]

### Step 2: Calculate the new average weight
According to the problem, the average weight increases by 1.5 kg when one person is replaced. Therefore, the new average weight becomes:
\[ \text{New average} = A + 1.5 \text{ kg} \]

### Step 3: Calculate the new total weight
The total weight of the 8 persons after the replacement will be:
\[ \text{New total weight} = 8(A + 1.5) = 8A + 12 \]

### Step 4: Relate the total weights
When the person weighing 65 kg is replaced by a new person (let's denote their weight as \( x \) kg), the new total weight can also be expressed as:
\[ \text{New total weight} = \text{Old total weight} - \text{Weight of replaced person} + \text{Weight of new person} \]
Substituting the known values, we have:
\[ 8A + 12 = 8A - 65 + x \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ 8A + 12 = 8A - 65 + x \]
Subtract \( 8A \) from both sides:
\[ 12 = -65 + x \]
Now, add 65 to both sides:
\[ 12 + 65 = x \]
\[ x = 77 \]

### Conclusion
The weight of the new person is \( 77 \) kg.

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