1997 AHSME Problems/Problem 8
Problem
Mientka Publishing Company prices its bestseller Where's Walter? as follows:
where is the number of books ordered, and is the cost in dollars of books. Notice that books cost less than books. For how many values of is it cheaper to buy more than books than to buy exactly books?
Solution
Clearly, the areas of concern are where the piecewise function shifts value.
Since , we want to find the least value of for which .
If , then , so for , , which is equivalent to . Thus, both and will be more expensive than .
Since , we want to find the least value of for which .
If , then , so for , we have , leading to . Thus, will be more expensive than .
Thus, there are values of where it's cheaper to buy more books, and the answer is .
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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