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

Latest revision as of 06:41, 15 November 2024

1 Problem
2 Solution 1
3 Solution 2
4 Video Solution by Math-X (First fully understand the problem!!!)
5 Video Solution (A Clever Explanation You’ll Get Instantly)
6 Video Solution 1 (easy to digest) by Power Solve
7 Video Solution 2 by SpreadTheMathLove
8 Video Solution by NiuniuMaths (Easy to understand!)
9 Video Solution by CosineMethod [🔥Fast and Easy🔥]
10 Video Solution by Interstigation
11 Video Solution by Dr. David
12 Video Solution by WhyMath
13 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?

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

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 by Math-X (First fully understand the problem!!!)

https://youtu.be/BaE00H2SHQM?si=XRr6hG8Mzai3OK-n&t=2749

~Math-X

Video Solution (A Clever Explanation You’ll Get Instantly)

https://youtu.be/5ZIFnqymdDQ?si=tmv7XmwLdPVqHRxy&t=1271

~hsnacademy

Video Solution 1 (easy to digest) by Power Solve

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

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

Video Solution by Dr. David

https://youtu.be/GTSragg_268

Video Solution by WhyMath

https://youtu.be/Gub5HfwfI1A

@@ Line 44: / Line 44: @@
 '''vladimir.shelomovskii@gmail.com, vvsss'''
+==Video Solution by Math-X (First fully understand the problem!!!)==
+https://youtu.be/BaE00H2SHQM?si=XRr6hG8Mzai3OK-n&t=2749
+~Math-X
 ==Video Solution (A Clever Explanation You’ll Get Instantly)==
@@ Line 53: / Line 58: @@
 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==
@@ Line 75: / Line 75: @@
 ==Video Solution by Dr. David==
 https://youtu.be/GTSragg_268
+==Video Solution by WhyMath==
+https://youtu.be/Gub5HfwfI1A
 ==See Also==
 {{AMC8 box|year=2024|num-b=11|num-a=13}}
 {{MAA Notice}}

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