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

Answer 1

6j + 1/3n = 134
1/3j + n = 31.....n = 31 - 1/3j

6j + 1/3(31 - 1/3j) = 134
6j + 31/3 - 1/9j = 134
6j - 1/9j = 134 - 31/3
54/9j - 1/9j = 402/3 - 31/3
53/9j = 371/3
j = 371/3 * 9/53
j = 1113/53
j = 21

n = 31 - 1/3j
n = 31 - 1/3(21)
n = 31 - 7
n = 24

so Jason (j) has 21 books and Nathan (n) has 24 books