Question

What is the weighted average of three points on a number line at 5, 10, and 25, with a ratio of 1:2:2 ?(1 point) Responses 18 18 10 10 11 11 15

Answer 1

To find the weighted average of the points 5, 10, and 25 with the weights in the ratio of 1:2:2, we follow these steps:

1. Assign weights to each point:
- Weight for the first point (5) = 1
- Weight for the second point (10) = 2
- Weight for the third point (25) = 2

2. Calculate the total weight:
\[
\text{Total Weight} = 1 + 2 + 2 = 5
\]

3. Calculate the weighted sum of the points:
\[
\text{Weighted Sum} = (5 \cdot 1) + (10 \cdot 2) + (25 \cdot 2)
\]
\[
= 5 + 20 + 50 = 75
\]

4. Calculate the weighted average:
\[
\text{Weighted Average} = \frac{\text{Weighted Sum}}{\text{Total Weight}} = \frac{75}{5} = 15
\]

Therefore, the weighted average of the points is \( \boxed{15} \).