Difference between revisions of "2024 AMC 8 Problems/Problem 12"
Hecker math (talk | contribs) (→Solution 1) |
(→Video Solution by NiuniuMaths (Easy to understand!)) |
||
Line 52: | Line 52: | ||
~NiuniuMaths | ~NiuniuMaths | ||
+ | |||
+ | == Video Solution by CosineMethod [🔥Fast and Easy🔥]== | ||
+ | |||
+ | https://www.youtube.com/watch?v=u5sC6tftndU | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2024|num-b=11|num-a=13}} | {{AMC8 box|year=2024|num-b=11|num-a=13}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 17:26, 27 January 2024
Contents
[hide]Problem
Rohan keeps a total of 90 guppies in 4 fish tanks.
- There is 1 more guppy in the 2nd tank than in the 1st tank.
- There are 2 more guppies in the 3rd tank than in the 2nd tank.
- There are 3 more guppies in the 4th tank than in the 3rd tank.
How many guppies are in the 4th tank?
Solution 1
Let denote the number of guppies in the first tank.
Then, we have the following for the number of guppies in the rest of the tanks:
- the number of guppies in the second tank
- the number of guppies in the third tank
- the number of guppies in the fourth tank
The number of guppies in all of the tanks combined is 90, so we can write the equation
.
Simplifying the equation gives
.
Solving the resulting equation gives , so the number of guppies in the fourth tank is .
Therefore, the correct answer is .
- C. Ren ~andliu766 (Minor edits)
Solution 2
Suppose, there is no guppies in the first tank. The numbers of guppies in another tanks are and totally guppies.
We need to add guppies into tanks or guppies in each tank.
So the number of guppies in the fourth tank is
vladimir.shelomovskii@gmail.com, vvsss
Video Solution 1 (easy to digest) by Power Solve
https://youtu.be/2UIVXOB4f0o?si=e1Q2EbdEfPB_Q5Ql&t=66
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=RRTxlduaDs8
Video Solution by NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=V-xN8Njd_Lc
~NiuniuMaths
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=u5sC6tftndU
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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.