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

1 answer

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.