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Difference between revisions of "2024 AMC 8 Problems/Problem 12"

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==Problem==
 
==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?
 +
 +
<math>\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 24 \qquad \textbf{(E)}\ 26</math>
 +
 
==Solution 1==
 
==Solution 1==
 +
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:
 +
 +
*<math>x + 1 =</math> the number of guppies in the second tank
 +
*<math>x + 1 + 2 =</math> the number of guppies in the third tank
 +
*<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
 +
 +
<math>x + x + 1 + x + 1 + 2 + x + 1 + 2 + 3 = 90</math>.
 +
 +
Simplifying the equation gives
 +
 +
<math>4x + 10 = 90</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
 +
~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==
 +
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

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?

$\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 24 \qquad \textbf{(E)}\ 26$

Solution 1

Let $x$ 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:

  • $x + 1 =$ the number of guppies in the second tank
  • $x + 1 + 2 =$ the number of guppies in the third tank
  • $x + 1 + 2 + 3 =$ 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

$x + x + 1 + x + 1 + 2 + x + 1 + 2 + 3 = 90$.

Simplifying the equation gives

$4x + 10 = 90$.

Solving the resulting equation gives $x = 20$, so the number of guppies in the fourth tank is $20 + 1 + 2 + 3 = 26$.

Therefore, the correct answer is $\boxed{\textbf{(E)}\ 26}$.

- 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 $1,3,$ and $6,$ or $10$ guppies in total.

We need to add $90 - 10 = 80$ guppies into $4$ tanks or $20$ guppies in each tank.

So the number of guppies in the fourth tank is $20 + 6 = \boxed{\textbf{(E)}\ 26}.$

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. AMC logo.png

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