2024 AMC 8 Problems/Problem 12: Difference between revisions

Latest revision as of 14:31, 18 August 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

Video solution by TheNeuralMathAcademy

https://youtu.be/f63MY1T2MgI&t=1031s

@@ Line 1: / Line 1: @@
+== 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?
+<math>\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 24 \qquad \textbf{(E)}\ 26</math>
+== 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:
+* The number of guppies in the second tank is <math>x+1</math>
+* The number of guppies in the third tank is <math>x+1+2</math>
+* The number of guppies in the fourth tank is <math>x+1+2+3</math>
+The number of guppies in all of the tanks combined is 90, so we can write the equation
+<cmath>(x)+(x+1)+(x+1+2)+(x+1+2+3) = 90.</cmath>
+Simplifying the equation gives
+<cmath>4x + 10 = 90.</cmath>
+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>.
+~ C. Ren, andliu766
+== 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>
+~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 ==
+[//youtu.be/BaE00H2SHQM?si=XRr6hG8Mzai3OK-n&t=2749 ~Math-X]
+==Video Solution 3 ==
+[//youtu.be/5ZIFnqymdDQ?si=tmv7XmwLdPVqHRxy&t=1271 ~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 ==
+[//www.youtube.com/watch?v=V-xN8Njd_Lc ~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 ==
+[https://youtu.be/x9CVizw-fz0 ~Thesmartgreekmathdude]
+== Video solution by TheNeuralMathAcademy ==
+https://youtu.be/f63MY1T2MgI&t=1031s
+== See Also ==
+{{AMC8 box|year=2024|num-b=11|num-a=13}}
+{{MAA Notice}}
+[[Category:Introductory Algebra Problems]]

2024 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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