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2023 AMC 8 Problems/Problem 3

Revision as of 10:46, 12 October 2024 by Thatsmartkid (talk | contribs) (→‎Solution 2: Estimation)

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 \[36 - \frac{2}{3} * 18\\ = 36 - 12\\ = 24\]. 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

*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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