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1997 AMC 12 Question 8

AMC12 · 1997 AMC 12

Question 8

Mientka Publishing Company prices its best seller *Where’s Walter?* as follows: $$
C(n)= \begin{cases} 12n, & 1\le n\le24,\\ 11n, & 25\le n\le48,\\ 10n, & 49\le n, \end{cases}
$$ where $n$ is the number of books ordered, and $C(n)$ is the cost in dollars of $n$ books. Notice that $25$ books cost less than $24$ books. For how many values of $n$ is it cheaper to buy more than $n$ books than to buy exactly $n$ books?
  1. $3$
  2. $4$
  3. $5$
  4. $6$
  5. $8$