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. how many books do jason’s and nathan’s collections have?

Sure, let me help you on this one.

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books is "(6*J)+(1/3*N)=134"

One-third of Jason's collection and Nathan's entire collection add up to 31 books is "(1/3*6)+N= 31

We need to multiply those equations by 18, and subtract one from another.

6j+18n=558
6j+1/3*n=134

After we subtract, we should get 53n/3=424.

Simplify that! n=24

Now you can substitute to answer the question. 

Nathan has 24 books and Jason has 21 books.