ok in this problem i see the answer, im just not sure how my book came up with the 4/9 or where it came from?

ok well let me post the problem....

in a certain reading group organized of only senior and junior students, 3/5 of the students are boys, and the ratio of seniors to juniors is 4:5. if 2/3 of girls are seniors, what fraction of the boys are juniors?

the answer in the book is 19/27

what the author did was create a table, at the bottom of his table he has A+B=4/9

where A = senior boys and B=senior girls, my question is where did the 4/9 come from?