Difference between revisions of "2024 AMC 8 Problems/Problem 12"
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| + | ==Problem== | ||
Rohan keeps a total of 90 guppies in 4 fish tanks. | Rohan keeps a total of 90 guppies in 4 fish tanks. | ||
| Line 10: | Line 11: | ||
==Solution 1== | ==Solution 1== | ||
| − | Let <math>x</math> | + | Let <math>x</math> 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: | Then, we have the following for the number of guppies in the rest of the tanks: | ||
| − | *<math>x</math> | + | *<math>x + 1 =</math> the number of guppies in the second tank |
| − | *<math>x | + | *<math>x + 1 + 2 =</math> the number of guppies in the third tank |
| − | *<math>x | + | *<math>x + 1 + 2 + 3 =</math> 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 | The number of guppies in all of the tanks combined is 90, so we can write the equation | ||
| − | <math>x | + | <math>x + x + 1 + x + 1 + 2 + x + 1 + 2 + 3 = 90</math>. |
Simplifying the equation gives | Simplifying the equation gives | ||
| − | + | <math>4x + 10 = 90</math>. | |
| − | Solving the resulting equation gives <math>x</math> | + | Solving the resulting equation gives <math>x = 20</math>, so the number of guppies in the fourth tank is <math>20 + 1 + 2 + 3 = 26</math>. |
| − | + | Therefore, the correct answer is <math>\boxed{\textbf{(E)}\ 26}</math>. | |
| − | - C. Ren, | + | - C. Ren |
| + | ~andliu766 (Minor edits) | ||
| + | |||
| + | ==Solution 2== | ||
| + | Suppose there are no guppies in the first tank. | ||
| + | |||
| + | Then, the number of guppies in the other tanks are <math>1,3,</math> and <math>6,</math> or <math>10</math> guppies in total. | ||
| + | |||
| + | We need to add <math>90 - 10 = 80</math> guppies into <math>4</math> tanks or <math>20</math> guppies in each tank. | ||
| + | |||
| + | So the number of guppies in the fourth tank is <math>20 + 6 = \boxed{\textbf{(E)}\ 26}.</math> | ||
| + | |||
| + | '''vladimir.shelomovskii@gmail.com, vvsss''' | ||
==Video Solution 1 (easy to digest) by Power Solve== | ==Video Solution 1 (easy to digest) by Power Solve== | ||
https://youtu.be/2UIVXOB4f0o?si=e1Q2EbdEfPB_Q5Ql&t=66 | https://youtu.be/2UIVXOB4f0o?si=e1Q2EbdEfPB_Q5Ql&t=66 | ||
| + | hello | ||
| + | |||
| + | ==Video Solution by Math-X (First fully understand the problem!!!)== | ||
| + | https://youtu.be/BaE00H2SHQM?si=XRr6hG8Mzai3OK-n&t=2749 | ||
| + | |||
| + | ~Math-X | ||
| + | |||
| + | ==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 | ||
| + | ==Video Solution by Interstigation== | ||
| + | https://youtu.be/ktzijuZtDas&t=1144 | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2024|num-b=11|num-a=13}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:29, 3 March 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Video Solution 1 (easy to digest) by Power Solve
- 5 Video Solution by Math-X (First fully understand the problem!!!)
- 6 Video Solution 2 by SpreadTheMathLove
- 7 Video Solution by NiuniuMaths (Easy to understand!)
- 8 Video Solution by CosineMethod [🔥Fast and Easy🔥]
- 9 Video Solution by Interstigation
- 10 See Also
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 the second tank
the number of guppies in the third tank
the number of guppies in the fourth tankThe 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 are no guppies in the first tank.
Then, the number of guppies in the other tanks are 
and 
or 
guppies in total.
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 hello
Video Solution by Math-X (First fully understand the problem!!!)
https://youtu.be/BaE00H2SHQM?si=XRr6hG8Mzai3OK-n&t=2749
~Math-X
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
Video Solution by Interstigation
https://youtu.be/ktzijuZtDas&t=1144
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. 
