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Math Help - Algebra - Number Theory

  1. #1
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    Algebra - Number Theory

    My local charity shop was selling off books at 3 paperbacks for $1, 2 hard back for $1 , and $2 for coffee table books, I spent $30 for 30 books and I bought at least one of each book . How many books of each type did I buy?
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  2. #2
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    Quote Originally Posted by ciccio View Post
    My local charity shop was selling off books at 3 paperbacks for $1, 2 hard back for $1 , and $2 for coffee table books, I spent $30 for 30 books and I bought at least one of each book . How many books of each type did I buy?
    If n_p>0, n_h>0 and n_c>0 denote the number of paper backs, hard backs and coffee table book bought we have:

    n_p+n_h+n_c=30

    and

    \frac{n_p}{3}+\frac{n_c}{2}+2n_c=30

    Also n_p is divisible by 3 and n_c is divisible by 2.

    Now a bit of trial and error should be sufficient to find the solution.

    CB
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