Question

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?

Answer 1

6j+$\frac{1}{3}$n=134

$\frac{1}{3} j+n=31$ you multiply this by 18

6j+18n=558
6j+1/3*n=134
___________(-)

53n/3=424 => 53n=1272 => n=24

You put n in the first equation:
6j+8=134
6j=126 => j=21

Final answer:  Nathan has 24 books and Jason 21.