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

 
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== Problem ==
  
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Rohan keeps 90 guppies in 4 fish tanks.
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* There is 1 more guppy in the 2nd tank than in the 1st tank.
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* There are 2 more guppies in the 3rd tank than in the 2nd tank.
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* There are 3 more guppies in the 4th tank than in the 3rd tank.
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How many guppies are in the 4th tank?
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<math>\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 24 \qquad \textbf{(E)}\ 26</math>
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== Solution 1 ==
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Let <math>x</math> denote the number of guppies in the first tank.
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Then, we have the following for the number of guppies in the rest of the tanks:
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* The number of guppies in the second tank is <math>x+1</math>
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* The number of guppies in the third tank is <math>x+1+2</math>
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* The number of guppies in the fourth tank is <math>x+1+2+3</math>
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The number of guppies in all of the tanks combined is 90, so we can write the equation
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<cmath>(x)+(x+1)+(x+1+2)+(x+1+2+3) = 90.</cmath>
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Simplifying the equation gives
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<cmath>4x + 10 = 90.</cmath>
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Solving the resulting equation gives <math>x = 20</math>, so the number of guppies in the fourth tank is <math>20+1+2+3 = \boxed{\textbf{(E)}\ 26}</math>.
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~ C. Ren, andliu766
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== Solution 2 ==
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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>
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~vvsss
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==Video by MathTalks 😉==
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https://youtu.be/qAwRUj2N46c?si=QDUY8ZUVFP29Eg4c
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  ~rc1219
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== Video Solution 1 by Central Valley Math Circle ==
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https://youtu.be/sldCPQRFgik
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~mr_mathman
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== Video Solution 2 ==
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[//youtu.be/BaE00H2SHQM?si=XRr6hG8Mzai3OK-n&t=2749 ~Math-X]
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==Video Solution 3 ==
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[//youtu.be/5ZIFnqymdDQ?si=tmv7XmwLdPVqHRxy&t=1271 ~hsnacademy]
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== Video Solution 4 by Power Solve ==
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https://youtu.be/2UIVXOB4f0o?si=e1Q2EbdEfPB_Q5Ql&t=66
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== Video Solution 5 by SpreadTheMathLove ==
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https://www.youtube.com/watch?v=RRTxlduaDs8
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==Video Solution 6 ==
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[//www.youtube.com/watch?v=V-xN8Njd_Lc ~NiuniuMaths]
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== Video Solution 7 by CosineMethod ==
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https://www.youtube.com/watch?v=u5sC6tftndU
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== Video Solution by Interstigation ==
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https://youtu.be/ktzijuZtDas&t=1144
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== Video Solution by Dr. David ==
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https://youtu.be/GTSragg_268
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==Video Solution by Daily Dose of Math ==
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[https://youtu.be/x9CVizw-fz0 ~Thesmartgreekmathdude]
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== See Also ==
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{{AMC8 box|year=2024|num-b=11|num-a=13}}
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{{MAA Notice}}
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[[Category:Introductory Algebra Problems]]

Latest revision as of 16:05, 2 June 2025

Problem

Rohan keeps 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:

  • The number of guppies in the second tank is $x+1$
  • The number of guppies in the third tank is $x+1+2$
  • The number of guppies in the fourth tank is $x+1+2+3$

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 $20+1+2+3 = \boxed{\textbf{(E)}\ 26}$.

~ C. Ren, andliu766

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 $20+6 = \boxed{\textbf{(E)}\ 26}.$

~vvsss

Video by MathTalks 😉

https://youtu.be/qAwRUj2N46c?si=QDUY8ZUVFP29Eg4c 

 ~rc1219


Video Solution 1 by Central Valley Math Circle

https://youtu.be/sldCPQRFgik ~mr_mathman

Video Solution 2

~Math-X

Video Solution 3

~hsnacademy

Video Solution 4 by Power Solve

https://youtu.be/2UIVXOB4f0o?si=e1Q2EbdEfPB_Q5Ql&t=66

Video Solution 5 by SpreadTheMathLove

https://www.youtube.com/watch?v=RRTxlduaDs8

Video Solution 6

~NiuniuMaths

Video Solution 7 by CosineMethod

https://www.youtube.com/watch?v=u5sC6tftndU

Video Solution by Interstigation

https://youtu.be/ktzijuZtDas&t=1144

Video Solution by Dr. David

https://youtu.be/GTSragg_268

Video Solution by Daily Dose of Math

~Thesmartgreekmathdude

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC Logo.png

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