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 ?

Jason's collection: 21 books.

Nathan's collection 24 books.

Step-by-step explanation:

Let number of books owned by Jason be j books and that for Nathan be n books.

So we have the system:

6j + 1/3 n = 134(1)

1/3j + n = 31(2)

Multiply the first equation by -3. We get:

-18j - n = -402(3)

Adding (2) + (3):

-53/3 j = -371

j = -371 * 3 / -53

j =  21.

Now substitute j = 21 in equation (2):

1/3(21) + n = 31

n = 31 - 7 = 24

n = 24.