Alas, The Pointless Things You Can Do With Marbles

Let the number of red marbles, green marbles, and blue marbles be $r, g, b$ respectively. From the first condition, we have that $r+b=16$ . From the second condition, we have that $g+b=17$ . From the last condition, we have that $r+g=19$ . Adding the first two together and subtracting the third gives $2b=14$ , or $b=7$ . Adding this to $r+g=19$ gives $r+g+b=\boxed{26}$ .