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.