From the given question, we are given the weight of two bags to be 10 2/3kg and 6 1/2kg.
The total weight of the bags will be equal to the sum of the individual weight as shown:
[tex]\text{Total w}eight=10\frac{2}{3}+6\frac{1}{2}[/tex]Convert to improper fraction to have:
[tex]\text{Total weight}=\frac{32}{3}+\frac{13}{2}[/tex]Find the Lowest Common Multiple and take the sum
[tex]\begin{gathered} \text{Total weight}=\frac{32}{3}+\frac{13}{2} \\ \text{Total weight}=\frac{32(2)+3(13)}{6} \\ \text{Total weight}=\frac{64+39}{6} \\ \text{Total weight}=\frac{103}{6} \end{gathered}[/tex]Convert the result into a mixed fraction to have:
[tex]\text{Total weight}=17\frac{1}{6}kg[/tex]Hence the total weight of the bag is 17 1/6kg