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2022 AMC 8 Problems/Problem 7: Difference between revisions

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<math>\textbf{(A) } 0.6 \qquad \textbf{(B) } 10 \qquad \textbf{(C) } 1800 \qquad \textbf{(D) } 7200 \qquad \textbf{(E) } 36000</math>
<math>\textbf{(A) } 0.6 \qquad \textbf{(B) } 10 \qquad \textbf{(C) } 1800 \qquad \textbf{(D) } 7200 \qquad \textbf{(E) } 36000</math>


==Solution==
==Solution 1==
 
Notice that the number of kilobits in this song is <math>4.2 \cdot 8000 = 8 \cdot 7 \cdot 6 \cdot 100.</math>
 
We must divide this by <math>56</math> in order to find out how many seconds this song would take to download: <math>\frac{\cancel{8}\cdot\cancel{7}\cdot6\cdot100}{\cancel{56}} = 600.</math>
 
Finally, we divide  this number by <math>60</math> because this is the number of <i><b>seconds</b></i> to get the answer <math>\frac{600}{60}=\boxed{\textbf{(B) } 10}.</math>
 
~wamofan
 
==Solution 2==
We seek a value of <math>x</math> that makes the following equation true, since every other quantity equals <math>1</math>.
 
<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>
Solving yields <math>x=\boxed{\textbf{(B) } 10}</math>.
 
-Benedict T (countmath1)
 
==Video Solution (A Clever Explanation You’ll Get Instantly)==
https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=751
~hsnacademy
 
==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==  
==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}}
[[Category:Introductory Algebra Problems]]

Latest revision as of 16:46, 4 June 2025

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 (A Clever Explanation You’ll Get Instantly)

https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=751 ~hsnacademy

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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