Difference between revisions of "2023 AMC 8 Problems/Problem 5"
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| − | + | ==Problem== | |
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| + | A lake contains <math>250</math> trout, along with a variety of other fish. When a marine biologist catches and releases a sample of <math>180</math> fish from the lake, <math>30</math> are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake? | ||
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| + | <math>\textbf{(A)}\ 1250 \qquad \textbf{(B)}\ 1500 \qquad \textbf{(C)}\ 1750 \qquad \textbf{(D)}\ 1800 \qquad \textbf{(E)}\ 2000</math> | ||
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| + | ==Solution== | ||
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| + | Note that <cmath>\frac{\text{number of trout}}{\text{total number of fish}} = \frac{30}{180} = \frac16.</cmath> So, the total number of fish is <math>6</math> times the number of trout. Since the lake contains <math>250</math> trout, there are <math>250\cdot6=\boxed{\textbf{(B)}\ 1500}</math> fish in the lake. | ||
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| + | ~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM | ||
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| + | ==Video Solution by Math-X (Let's first Understand the question)== | ||
| + | https://youtu.be/Ku_c1YHnLt0?si=daQltLOjgTuUiFTM&t=593 ~Math-X | ||
| + | |||
| + | ==Video Solution by Magic Square== | ||
| + | https://youtu.be/-N46BeEKaCQ?t=5308 | ||
| + | |||
| + | ==Video Solution by SpreadTheMathLove== | ||
| + | https://www.youtube.com/watch?v=EcrktBc8zrM | ||
| + | ==Video Solution by Interstigation== | ||
| + | https://youtu.be/DBqko2xATxs&t=345 | ||
| + | |||
| + | ==Video Solution by WhyMath== | ||
| + | https://youtu.be/J23Ljt3uV-8 | ||
| + | |||
| + | ~savannahsolver | ||
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| + | ==Video Solution by harungurcan== | ||
| + | https://www.youtube.com/watch?v=35BW7bsm_Cg&t=547s | ||
| + | |||
| + | ~harungurcan | ||
| + | |||
| + | ==Simple Solution by MathTalks_Now== | ||
| + | * https://studio.youtube.com/video/PMOeiGLkDH0/edit | ||
| + | |||
| + | ==Video Solution (How to CREATIVELY THINK!!!)== | ||
| + | https://youtu.be/Rhg5mu7pdNU | ||
| + | |||
| + | ~Education the Study of Everything | ||
| + | |||
| + | ==Video Solution by Dr. David== | ||
| + | https://youtu.be/n78DeBJNfjY | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2023|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 10:33, 12 October 2024
Contents
- 1 Problem
- 2 Solution
- 3 Video Solution by Math-X (Let's first Understand the question)
- 4 Video Solution by Magic Square
- 5 Video Solution by SpreadTheMathLove
- 6 Video Solution by Interstigation
- 7 Video Solution by WhyMath
- 8 Video Solution by harungurcan
- 9 Simple Solution by MathTalks_Now
- 10 Video Solution (How to CREATIVELY THINK!!!)
- 11 Video Solution by Dr. David
- 12 See Also
Problem
A lake contains 
trout, along with a variety of other fish. When a marine biologist catches and releases a sample of 
fish from the lake, 
are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?
Solution
Note that ![\[\frac{\text{number of trout}}{\text{total number of fish}} = \frac{30}{180} = \frac16.\]](http://latex.artofproblemsolving.com/c/2/d/c2d56c81b6970c98c737fea028a7743c6d3616ec.png)
So, the total number of fish is 
times the number of trout. Since the lake contains trout, there are 
fish in the lake.
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM
Video Solution by Math-X (Let's first Understand the question)
https://youtu.be/Ku_c1YHnLt0?si=daQltLOjgTuUiFTM&t=593 ~Math-X
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=5308
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=EcrktBc8zrM
Video Solution by Interstigation
https://youtu.be/DBqko2xATxs&t=345
Video Solution by WhyMath
~savannahsolver
Video Solution by harungurcan
https://www.youtube.com/watch?v=35BW7bsm_Cg&t=547s
~harungurcan
Simple Solution by MathTalks_Now
Video Solution (How to CREATIVELY THINK!!!)
~Education the Study of Everything
Video Solution by Dr. David
See Also
| 2023 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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. 
