Six times jasons collection of books and one-third of nathans collection add up to 134 books one-third of jasons collection and nathans entire collection add up to 31

6j + 1/3n = 134...multiply by 318j + n = 402
1/3j + n = 31multiply by 3j + 3n = 93

the multiplying by 3 is optional...I just did it because it is easier to work with equations when there are no fractions.

18j + n = 402multiply by -3
j + 3n = 93

-54j - 3n = - 1206 (result of multiplying by -3)
j + 3n = 93
add
-53j = - 1113
j = -1113/-53
j = 21

j + 3n = 93
21 + 3n = 93
3n = 93 - 21
3n = 72
n = 72/3
n = 24

so Jasons collection (j) consists of 21 books and Nathans collection (n) consists of 24 books