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 = 31n = 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