Problem:
Mientka Publishing Company prices its best seller 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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The cost of books is . The cost of books is , while and books cost and , respectively. Thus it is cheaper to buy books than or books. Similarly, books cost less than , or books. In these six cases the total cost is reduced by ordering more books. There are no other cases.
A discount of per book is given on orders of at least books. This discount is larger than , the cost of two books at the regular price. Thus, and are two values of for which it is cheaper to order more books. Similarly, we receive an additional discount per book when we buy at least books. This discount would enable us to buy more books at per book, so there are more values of , and , for a total of values.