2023 AMC 8 Problems/Problem 14
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[hide]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.)
Solution 1
Most stamps make You have of each coin, nickles, dimes and quarters.
If we want to have the most amount of stamps we have to have the most amount of smaller value coins. We can use nickels and dimes to bring our total cost to . However when we try to use quarters the cents don’t fit evenly, so we have to give back cents in order to make the quarter amount the most efficient way to do this is give back a dime and a nickel to have coins used so far. Now we just use quarters to get a grand total of .
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat
Solution 2
The value of his entire stamp collect is dollars. To make with stamps, he should remove cents worth of stamps with as few stamps as possible. To do this, he should start by removing as many cent stamps as possible, as they have the greatest denomination. He can remove at most of these stamps. He still has to remove cents worth of stamps. This can be done with one and cent stamp. In total, he has stamps in his entire collect. As a result, the maximum number of stamps he can use is .
~pianoboy
~MathFun1000 (Rewrote for clarity and formatting)
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4280
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AJHSME/AMC 8 Problems and Solutions |
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