Difference between revisions of "2023 AMC 8 Problems/Problem 3"
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− | + | ==Problem== | |
− | apex304, SohumUttamchandani, wuwang2002, TaeKim. | + | |
+ | <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> | ||
+ | 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{(D)}\ 32 \qquad \textbf{(E)}\ 35</math> | ||
+ | |||
+ | == Solution == | ||
+ | |||
+ | By substitution, we have | ||
+ | <cmath>\begin{align*} | ||
+ | (\text{wind chill}) &= 36 - 0.7 \times 18 \\ | ||
+ | &= 36 - 12.6 \\ | ||
+ | &= 23.4 \\ | ||
+ | &\approx \boxed{\textbf{(B)}\ 23}. | ||
+ | \end{align*}</cmath> | ||
+ | ~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 <math>36 - \frac{2}{3} * 18</math>, which is <math>36 - 12 = 24</math>. 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 | ||
+ | |||
+ | ==*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 | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2023|num-b=2|num-a=4}} | ||
+ | {{MAA Notice}} |
Latest revision as of 13:31, 17 January 2024
Contents
- 1 Problem
- 2 Solution
- 3 Solution 2: Estimation
- 4 *Simple Video Explanation by MathTalks_Now*
- 5 Video Solution (How to Creatively THINK!!!)
- 6 Video Solution by Math-X (Smart and Simple)
- 7 Video Solution by Magic Square
- 8 Video Solution by SpreadTheMathLove
- 9 Video Solution by Interstigation
- 10 Video Solution by WhyMath
- 11 Video Solution by harungurcan
- 12 See Also
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
where temperature is measured in degrees Fahrenheit
and the wind speed is measured in miles per hour (mph). Suppose the air temperature is
and the wind speed is
mph. Which of the following is closest to the approximate wind chill?
Solution
By substitution, we have
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM
Solution 2: Estimation
is very close to
- therefore, we can substitute
into the equation to get
, which is
. As
is slightly less than
, the correct answer is slightly less than
. Therefore, the answer is
.
~TheGoldenRetriever
*Simple Video Explanation by MathTalks_Now*
https://studio.youtube.com/video/PMOeiGLkDH0/edit
Video Solution (How to Creatively THINK!!!)
~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
~savannahsolver
Video Solution by harungurcan
https://www.youtube.com/watch?v=35BW7bsm_Cg&t=230s
~harungurcan
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.