First let's convert the decimal numbers to mixed numbers:
[tex]\begin{gathered} 3.4=3+0.4=3+\frac{4}{10}=3+\frac{2}{5}=3\frac{2}{5} \\ 1.75=1+0.75=1+\frac{75}{100}=1+\frac{3}{4}=1\frac{3}{4} \\ 2.25=2+0.25=2+\frac{25}{100}=2+\frac{1}{4}=2\frac{1}{4} \end{gathered}[/tex]
Now, adding all the numbers, we have:
[tex]\begin{gathered} (3+\frac{2}{5})+(3+\frac{1}{5})+(1+\frac{3}{4})+(2+\frac{1}{4})+(1+\frac{7}{10}) \\ =(3+3+1+2+1)+(\frac{2}{5}+\frac{1}{5}+\frac{3}{4}+\frac{1}{4}+\frac{7}{10}) \\ =10+(\frac{3}{5}+1+\frac{7}{10}) \\ =11+(\frac{6}{10}+\frac{7}{10}) \\ =11+\frac{13}{10} \\ =12+\frac{3}{10}=12\frac{3}{10} \end{gathered}[/tex]
So the correct option is B.
