To find the weighted average, you can use the formula:
\[ \text{Weighted Average} = \left( w_1 \cdot x_1 + w_2 \cdot x_2 \right) / (w_1 + w_2) \]
where \( w_1 \) and \( w_2 \) are the weights, and \( x_1 \) and \( x_2 \) are the corresponding values.
In this case:
- \( x_1 = 1 \), \( w_1 = \frac{2}{5} \)
- \( x_2 = 8 \), \( w_2 = \frac{3}{5} \)
Now, we calculate the weighted average:
\[ \text{Weighted Average} = \left( \frac{2}{5} \cdot 1 + \frac{3}{5} \cdot 8 \right) / \left( \frac{2}{5} + \frac{3}{5} \right) \]
Calculating the numerator:
\[ \frac{2}{5} \cdot 1 + \frac{3}{5} \cdot 8 = \frac{2}{5} + \frac{24}{5} = \frac{2 + 24}{5} = \frac{26}{5} \]
Calculating the denominator:
\[ \frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1 \]
Now, substituting these values back into the weighted average formula gives:
\[ \text{Weighted Average} = \frac{\frac{26}{5}}{1} = \frac{26}{5} = 5.2 \]
So, the weighted average of the numbers 1 and 8 is 5.2.