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Difference between revisions of "2022 AMC 8 Problems/Problem 7"

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~wamofan
 
~wamofan
  
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==Solution 2==
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We seek a value of <math>x</math> that makes the following equation true, since every other quantity equals <math>1</math>.
  
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==Solution 2 (Dimensional Analysis)==
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<cmath>\frac{x\ \text{min}}{4.2\ \text{mb}} \cdot \frac{56\ \text{kb}}{1\ \text{sec}} \cdot \frac{1\ \text{mb}}{8000\ \text{kb}} \cdot \frac{60\ \text{sec}}{1\ \text{min}} = 1.</cmath>
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We seek a value of <math>x</math> that makes the following equation true, since evrery other quantity equals <math>1</math>.
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Solving yields <math>x=\boxed{\textbf{(B) } 10}</math>.
  
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<cmath>\frac{x\ \text{min}}{4.2\ \text{mb}} \cdot \frac{56\ \text{kb}}{1\ \text{sec}} \cdot \frac{1\ \text{mb}}{8000\ \text{kb}} \cdot \frac{60\ \text{sec}}{1\ \text{min}} = 1</cmath>
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-Benedict T (countmath1)
  
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Solving yields <math>x=\boxed{\textbf{(B) } 10}</math>
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==Video Solution by Math-X (First understand the problem!!!)==
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https://youtu.be/oUEa7AjMF2A?si=ZRtIWQMPPOjOX9fB&t=822
 +
 
 +
~Math-X
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 +
==Video Solution (THINKING CREATIVELY!!!)==
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https://youtu.be/ZXMYmDPOypo
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 +
~Education, the Study of Everything
  
 
==Video Solution==
 
==Video Solution==
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~Interstigation
 
~Interstigation
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==Video Solution==
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https://youtu.be/1xspUFoKDnU?t=65
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~STEMbreezy
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 +
==Video Solution==
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https://youtu.be/scSofI5OqkQ
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~savannahsolver
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==Video Solution==
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https://youtu.be/jmblFtkaKpc
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~harungurcan
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==Video Solution by Dr. David==
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https://youtu.be/2GNMZKWqfyw
  
 
==See Also==  
 
==See Also==  
 
{{AMC8 box|year=2022|num-b=6|num-a=8}}
 
{{AMC8 box|year=2022|num-b=6|num-a=8}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 20:28, 25 November 2024

Problem

When the World Wide Web first became popular in the $1990$s, download speeds reached a maximum of about $56$ kilobits per second. Approximately how many minutes would the download of a $4.2$-megabyte song have taken at that speed? (Note that there are $8000$ kilobits in a megabyte.)

$\textbf{(A) } 0.6 \qquad \textbf{(B) } 10 \qquad \textbf{(C) } 1800 \qquad \textbf{(D) } 7200 \qquad \textbf{(E) } 36000$

Solution 1

Notice that the number of kilobits in this song is $4.2 \cdot 8000 = 8 \cdot 7 \cdot 6 \cdot 100.$

We must divide this by $56$ in order to find out how many seconds this song would take to download: $\frac{\cancel{8}\cdot\cancel{7}\cdot6\cdot100}{\cancel{56}} = 600.$

Finally, we divide this number by $60$ because this is the number of seconds to get the answer $\frac{600}{60}=\boxed{\textbf{(B) } 10}.$

~wamofan

Solution 2

We seek a value of $x$ that makes the following equation true, since every other quantity equals $1$.

\[\frac{x\ \text{min}}{4.2\ \text{mb}} \cdot \frac{56\ \text{kb}}{1\ \text{sec}} \cdot \frac{1\ \text{mb}}{8000\ \text{kb}} \cdot \frac{60\ \text{sec}}{1\ \text{min}} = 1.\] Solving yields $x=\boxed{\textbf{(B) } 10}$.

-Benedict T (countmath1)

Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/oUEa7AjMF2A?si=ZRtIWQMPPOjOX9fB&t=822

~Math-X

Video Solution (THINKING CREATIVELY!!!)

https://youtu.be/ZXMYmDPOypo

~Education, the Study of Everything

Video Solution

https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=475

~Interstigation

Video Solution

https://youtu.be/1xspUFoKDnU?t=65

~STEMbreezy

Video Solution

https://youtu.be/scSofI5OqkQ

~savannahsolver

Video Solution

https://youtu.be/jmblFtkaKpc

~harungurcan

Video Solution by Dr. David

https://youtu.be/2GNMZKWqfyw

See Also

2022 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 6 		Followed by
Problem 8
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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