Difference between revisions of "2023 AMC 8 Problems/Problem 14"
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~harungurcan | ~harungurcan | ||
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| + | ==Video Solution (Solve under 60 seconds!!!)== | ||
| + | https://youtu.be/6O5UXi-Jwv4?si=KvvABit-3-ZtX7Qa&t=633 | ||
| + | |||
| + | ~hsnacademy | ||
| + | |||
| + | ==Video Solution by Dr. David== | ||
| + | https://youtu.be/bVA6Sx4mbdM | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2023|num-b=13|num-a=15}} | {{AMC8 box|year=2023|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 00:10, 28 October 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Video Solution (CREATIVE THINKING!!!)
- 5 Video Solution by Math-X (Smart and Simple)
- 6 Animated Video Solution
- 7 Video Solution by Magic Square
- 8 Video Solution by Interstigation
- 9 Video Solution by harungurcan
- 10 Video Solution (Solve under 60 seconds!!!)
- 11 Video Solution by Dr. David
- 12 See Also
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
Let's use the most stamps to make 
We have of each stamp, -cent (nickels), -cent (dimes), and -cent (quarters).
If we want the highest number of stamps, we must have the highest number of the smaller value stamps (like the coins above). 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 to make the quarter amount 
. The most efficient way to do this is to give back a -cent (dime) stamp and a -cent (nickel) stamp to have 
stamps used so far. Now, we just use 
quarters to get a grand total of 
.
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, InterstellerApex, mahika99
Solution 2
The value of his entire stamp collection 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 collection. As a result, the maximum number of stamps he can use is 
.
~pianoboy
~MathFun1000 (Rewrote for clarity and formatting)
~vadava_lx (minor edits)
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution by Math-X (Smart and Simple)
https://youtu.be/Ku_c1YHnLt0?si=GHLp1q_7Le68a4rJ&t=2454 ~Math-X note from InterstellerApex: this is wrong, he didn’t choose the correct answer. :(
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4280
Video Solution by Interstigation
https://youtu.be/DBqko2xATxs&t=1435
Video Solution by harungurcan
https://www.youtube.com/watch?v=VqN7c5U5o98&t=449s
~harungurcan
Video Solution (Solve under 60 seconds!!!)
https://youtu.be/6O5UXi-Jwv4?si=KvvABit-3-ZtX7Qa&t=633
~hsnacademy
Video Solution by Dr. David
See Also
| 2023 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
