Question

Two points are on a number line at 2 and 6. The original weighted average is 4, with a ratio of 1:1 . What will be the new weighted average if the ratio changes to 2:1 ?(1 point) Responses 4 4 2.67 2.67 3.3¯¯¯ 3 point repeating 3 5

Answer 1

To find the new weighted average when the ratio changes from 1:1 to 2:1, we can follow these steps:

1. **Identify the points and their original weights**:
- Points: 2 and 6
- Original weights (for ratio 1:1): Both weights = 1

2. **Calculate the original weighted average**:
\[
\text{Original Weighted Average} = \frac{2 \cdot 1 + 6 \cdot 1}{1 + 1} = \frac{2 + 6}{2} = \frac{8}{2} = 4
\]

3. **Change the ratio to 2:1**:
- New weights: Weight of point 2 = 2, Weight of point 6 = 1

4. **Calculate the new weighted average**:
\[
\text{New Weighted Average} = \frac{2 \cdot 2 + 6 \cdot 1}{2 + 1} = \frac{4 + 6}{3} = \frac{10}{3} \approx 3.33
\]

Thus, the new weighted average is \( \frac{10}{3} \) or approximately \( 3.33 \).

The correct answer is **3.3 (point repeating)**.