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)

Question

1. 5

2. 3.3

3. 4

4. 2.67

Answer 1

To find the new weighted average when the ratio changes from 1:1 to 2:1, we start by calculating the original weighted average.

Given the points are 2 and 6, and they are weighted equally (1:1), the original weighted average can be calculated as follows:

\[ \text{Weighted Average} = \frac{(1 \cdot 2) + (1 \cdot 6)}{1 + 1} = \frac{2 + 6}{2} = \frac{8}{2} = 4 \]

Now, we are asked to find the new weighted average with a ratio of 2:1. This means we will have:

• The number 2 with a weight of 2
• The number 6 with a weight of 1

The new weighted average is calculated as follows:

\[ \text{New Weighted Average} = \frac{(2 \cdot 2) + (1 \cdot 6)}{2 + 1} = \frac{4 + 6}{3} = \frac{10}{3} \approx 3.33 \]

Thus, the new weighted average is approximately 3.3.

The answer is:

2. 3.3