Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books. One-third of Jason's collection and Nathan's entire collection add up to 31 books. The number of books in Jason's collection is, and the number of books in Nathan's collection is.

6j + 1/3n = 134

1/3j + n = 31 ... n = 31 - 1/3j

6j + 1/3 (31 - 1/3j) = 134

6j + 31/3 - 1/9j = 134

6j - 1/9j = 134 - 31/3

54/9j - 1/9j = 402/3 - 31/3

53/9j = 371/3

j = 371/3 * 9/53

j = 1113/53

j = 21

n = 31 - 1/3j

n = 31 - 1/3 (21)

n = 31 - 7

n = 24

so Jason (j) has 21 books and Nathan (n) has 24 books