1985 AJHSME Problem 18
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Problem
Nine copies of a certain pamphlet cost less than 
while ten copies of the same pamphlet (at the same price) cost more than 
. How much does one copy of this pamphlet cost?
Solution
Let the cost of one pamphlet be 
Then we have 
and 
Multiply both inequalities as follows:
![\[9x < 10 \rightarrow 900x < 1000\]](http://latex.artofproblemsolving.com/8/6/7/867e58bb7352b1fcdf095939f18a853c08dd933a.png)
![\[10x > 11 \rightarrow 900x > 990\]](http://latex.artofproblemsolving.com/6/b/4/6b4641e19abf785b49301ba7863024593de9fba2.png)
The only answer choice that satisfies both inequalities is 
