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 ?


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Answer 1

Jason's collection: 21 books.

Nathan's collection 24 books.

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.