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Difference between revisions of "2023 AMC 8 Problems/Problem 3"

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<i>Wind chill</i> is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation
 
<i>Wind chill</i> is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation
 
<cmath>(\text{wind chill}) = (\text{air temperature}) - 0.7 \times (\text{wind speed}),</cmath>
 
<cmath>(\text{wind chill}) = (\text{air temperature}) - 0.7 \times (\text{wind speed}),</cmath>
−
where temperature is measured in degrees Fahrenheit <math>(^{\circ}\text{F})</math> and and the wind speed is measured in miles per hour (mph). Suppose the air temperature is <math>36^{\circ}\text{F} </math> and the wind speed is <math>18</math> mph. Which of the following is closest to the approximate wind chill?
+
where temperature is measured in degrees Fahrenheit <math>(^{\circ}\text{F})</math> and the wind speed is measured in miles per hour (mph). Suppose the air temperature is <math>36^{\circ}\text{F} </math> and the wind speed is <math>18</math> mph. Which of the following is closest to the approximate wind chill?
  
−
<math>\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 23 \qquad \textbf{(C)}\ 28 \qquad \textbf{(B)}\ 32 \qquad \textbf{(E)}\ 35</math>
+
<math>\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 23 \qquad \textbf{(C)}\ 28 \qquad \textbf{(D)}\ 32 \qquad \textbf{(E)}\ 35</math>
  
 
== Solution ==
 
== Solution ==
Line 16: Line 16:
 
&\approx \boxed{\textbf{(B)}\ 23}.
 
&\approx \boxed{\textbf{(B)}\ 23}.
 
\end{align*}</cmath>
 
\end{align*}</cmath>
−
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, lpieleanu, MRENTHUSIASM
+
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM
 +
 
 +
== Solution 2 (Estimation) ==
 +
 
 +
<math>0.7</math> is very close to <math>\frac{2}{3}</math> - therefore, we can substitute <math>\frac{2}{3}</math> into the equation to get <cmath>36 - \frac{2}{3} \cdot 18 = 36 - 12 = 24.</cmath> As <math>\frac{2}{3}</math> is slightly less than <math>0.7</math>, the correct answer is slightly less than <math>24</math>. Therefore, the answer is <math>\boxed{\textbf{(B)}\ 23}</math>.
 +
 
 +
~TheGoldenRetriever
 +
 
 +
==Solution 3==
 +
 
 +
0.7 is equivalent to 7/10. 7/10 times 18 is 126/10, which is 12.6. Since the air temperature is 36 degrees Fahrenheit, 36 - 12.6 is 23.4, which is the closest to <math>\boxed{\textbf{(B)}\ 23}</math>.
 +
 
 +
~AliceDubbleYou
 +
 
 +
==*Simple Video Explanation by MathTalks_Now*==
 +
https://studio.youtube.com/video/PMOeiGLkDH0/edit
 +
 
 +
==Video Solution (How to Creatively THINK!!!) ==
 +
https://youtu.be/lVgjbLPvzt8
 +
 
 +
~Education the Study of everything
 +
 
 +
==Video Solution by Math-X (Smart and Simple)==
 +
https://youtu.be/Ku_c1YHnLt0?si=OLOhPCvcHiZhLK6e&t=218 ~Math-X
  
 
==Video Solution by Magic Square==
 
==Video Solution by Magic Square==
 
https://youtu.be/-N46BeEKaCQ?t=5606
 
https://youtu.be/-N46BeEKaCQ?t=5606
 +
 +
==Video Solution by SpreadTheMathLove==
 +
https://www.youtube.com/watch?v=EcrktBc8zrM
 +
==Video Solution by Interstigation==
 +
https://youtu.be/DBqko2xATxs&t=149
 +
 +
==Video Solution by WhyMath==
 +
https://youtu.be/k5hyZnmya14
 +
 +
~savannahsolver
 +
 +
==Video Solution by harungurcan==
 +
https://www.youtube.com/watch?v=35BW7bsm_Cg&t=230s
 +
 +
~harungurcan
 +
 +
==Video Solution by Dr. David==
 +
https://youtu.be/O6CLQ5Lks3s
  
 
==See Also==  
 
==See Also==  
 
{{AMC8 box|year=2023|num-b=2|num-a=4}}
 
{{AMC8 box|year=2023|num-b=2|num-a=4}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 20:37, 27 October 2024

Problem

Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation \[(\text{wind chill}) = (\text{air temperature}) - 0.7 \times (\text{wind speed}),\] where temperature is measured in degrees Fahrenheit $(^{\circ}\text{F})$ and the wind speed is measured in miles per hour (mph). Suppose the air temperature is $36^{\circ}\text{F}$ and the wind speed is $18$ mph. Which of the following is closest to the approximate wind chill?

$\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 23 \qquad \textbf{(C)}\ 28 \qquad \textbf{(D)}\ 32 \qquad \textbf{(E)}\ 35$

Solution

By substitution, we have \begin{align*} (\text{wind chill}) &= 36 - 0.7 \times 18 \\ &= 36 - 12.6 \\ &= 23.4 \\ &\approx \boxed{\textbf{(B)}\ 23}. \end{align*} ~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM

Solution 2 (Estimation)

$0.7$ is very close to $\frac{2}{3}$ - therefore, we can substitute $\frac{2}{3}$ into the equation to get \[36 - \frac{2}{3} \cdot 18 = 36 - 12 = 24.\] As $\frac{2}{3}$ is slightly less than $0.7$, the correct answer is slightly less than $24$. Therefore, the answer is $\boxed{\textbf{(B)}\ 23}$.

~TheGoldenRetriever

Solution 3

0.7 is equivalent to 7/10. 7/10 times 18 is 126/10, which is 12.6. Since the air temperature is 36 degrees Fahrenheit, 36 - 12.6 is 23.4, which is the closest to $\boxed{\textbf{(B)}\ 23}$.

~AliceDubbleYou

*Simple Video Explanation by MathTalks_Now*

https://studio.youtube.com/video/PMOeiGLkDH0/edit

Video Solution (How to Creatively THINK!!!)

https://youtu.be/lVgjbLPvzt8

~Education the Study of everything

Video Solution by Math-X (Smart and Simple)

https://youtu.be/Ku_c1YHnLt0?si=OLOhPCvcHiZhLK6e&t=218 ~Math-X

Video Solution by Magic Square

https://youtu.be/-N46BeEKaCQ?t=5606

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=EcrktBc8zrM

Video Solution by Interstigation

https://youtu.be/DBqko2xATxs&t=149

Video Solution by WhyMath

https://youtu.be/k5hyZnmya14

~savannahsolver

Video Solution by harungurcan

https://www.youtube.com/watch?v=35BW7bsm_Cg&t=230s

~harungurcan

Video Solution by Dr. David

https://youtu.be/O6CLQ5Lks3s

See Also

2023 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
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

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