Problem:
Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas would like to cover the package with a large number of stamps. Suppose he has a collection of -cent, -cent, and -cent stamps, with exactly of each type. What is the greatest number of stamps Nicolas can use to make exactly in postage? (Note: The amount corresponds to dollars and cents. One dollar is worth cents.)
Answer Choices:
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Solution:
Note that we want to get cents. Let us try to see if it is possible to use up all of the -cent and -cent stamps. All of these two types of stamps combined would be worth cents. We then would need cents, which cannot be created with just -cent stamps. We can, however, make cents with -cent stamps. Using only each of -cent and -cent stamps would total cents. This means we would then need cents. This can be achieved with -cent stamps. This lets us use stamps.
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions