The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.

Options

A. 80
B. 67
C. 85
D. 20

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the Initial Situation
Let the total weight of the 8 women before the replacement be \( Y \). The average weight of these women can be expressed as:
\[ \text{Average weight} = \frac{Y}{8} \]

### Step 2: Determine the New Average Weight
According to the problem, the average weight increases by 2.5 kg when a new woman replaces one of the existing women. Therefore, the new average weight becomes:
\[ \text{New Average weight} = \frac{Y}{8} + 2.5 \]

### Step 3: Calculate the Total Weight After Replacement
The total weight after replacing the woman weighing 65 kg with the new woman (whose weight we will denote as \( x \)) can be expressed as:
\[ \text{New Total Weight} = Y - 65 + x \]

### Step 4: Set Up the Equation
Since the new average weight is also equal to the new total weight divided by 8, we can set up the equation:
\[ \frac{Y - 65 + x}{8} = \frac{Y}{8} + 2.5 \]

### Step 5: Eliminate the Denominator
To eliminate the denominator, multiply both sides of the equation by 8:
\[ Y - 65 + x = Y + 20 \]

### Step 6: Simplify the Equation
Now, simplify the equation:
\[ Y - 65 + x = Y + 20 \]
Subtract \( Y \) from both sides:
\[ -65 + x = 20 \]

### Step 7: Solve for \( x \)
Now, add 65 to both sides to solve for \( x \):
\[ x = 20 + 65 \]
\[ x = 85 \]

### Conclusion
The weight of the new woman is \( 85 \) kg.