17. Two thirds in addition (to the unknown), $\frac{1}{3}$ in subtraction, 10 remains (i.e., two thirds of the unknown are added to it, and one third is subtracted from the resulting sum. The remainder is 10).
17. The equation will be:

$$
x+\frac{2}{3} x-\frac{1}{3}\left(x+\frac{2}{3} x\right)=10 ; x=9
$$

$\begin{array}{ll}\text { 18. } x=\frac{3}{10} ; x=\frac{15}{53} & \text { 19. } 4 \frac{1}{6} \text {. }\end{array}$