# Thread: Algebra - Number Theory

1. ## 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?

2. Originally Posted by ciccio
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