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 .

The number of books in Jason's collection is 21 , and the number of books in Nathan's collection is 24 .

Step-by-step explanation:

Let x represent the number of books Jason has and y represents the number of books Nathan has .

Then , According to the question , we have

Multiply 9 in equation (1) and and 3 in equation (2), we get

Subtract equation (4) from equation (3), we get

Divide 53 on both sides, we get

Put the value of x in (2), we get

Hence, The number of books in Jason's collection is 21 , and the number of books in Nathan's collection is 24 .