Question

Find the weighted average of points P=5 and Q=25 on a number line, given the ratio of 2:3 .

Answer 1

To find the weighted average of points P and Q given the ratio of 2:3, we use the formula for the weighted average:

\[
\text{Weighted Average} = \frac{(w_1 \cdot x_1 + w_2 \cdot x_2)}{(w_1 + w_2)}
\]

where \(w_1\) and \(w_2\) are the weights, and \(x_1\) and \(x_2\) are the points.

In this case:
- \(x_1 = P = 5\)
- \(x_2 = Q = 25\)
- \(w_1 = 2\)
- \(w_2 = 3\)

Now we can substitute the values into the formula:

\[
\text{Weighted Average} = \frac{(2 \cdot 5 + 3 \cdot 25)}{(2 + 3)}
\]

Calculating the numerator:

\[
2 \cdot 5 = 10
\]
\[
3 \cdot 25 = 75
\]
\[
10 + 75 = 85
\]

Now the denominator:

\[
2 + 3 = 5
\]

Putting it all together:

\[
\text{Weighted Average} = \frac{85}{5} = 17
\]

Thus, the weighted average of points P and Q in the ratio of 2:3 is **17**.