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Difference between revisions of "2020 AMC 8 Problems/Problem 2"
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==Problem 2==
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==Problem==
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Four friends do yardwork for their neighbors over the weekend, earning <math>\$15, \$20, \$25,</math> and <math>\$40,</math> respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned <math>\$40</math> give to the others?
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Four friends do yardwork for their neighbors over the weekend, earning <math>\$15, \$20, \$25,</math> and <math>\$40,</math> respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned <math>\$40</math> give to the others?
  
 
<math>\textbf{(A) }\$5 \qquad \textbf{(B) }\$10 \qquad \textbf{(C) }\$15 \qquad \textbf{(D) }\$20 \qquad \textbf{(E) }\$25</math>
 
<math>\textbf{(A) }\$5 \qquad \textbf{(B) }\$10 \qquad \textbf{(C) }\$15 \qquad \textbf{(D) }\$20 \qquad \textbf{(E) }\$25</math>
  
 
==Solution==
 
==Solution==
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First we average <math>15,20,25,40</math> to get <math>25</math>. Thus, <math>40 - 25 = \boxed{\textbf{(C) }15.}</math>. ~~Spaced_Out
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The friends earn <math>\$\left(15+20+25+40\right)=\$100</math> in total. Since they decided to split their earnings equally, it follows that each person will get <math>\$\left(\frac{100}{4}\right)=\$25</math>. Since the friend who earned <math>\$40</math> will need to leave with <math>\$25</math>, he will have to give <math>\$\left(40-25\right)=\boxed{\textbf{(C) }\$15}</math> to the others.
  
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==Solution 2==
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==Video Solution by NiuniuMaths (Easy to understand!)==
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The total earnings for the four friends is <math>\$15+\$20+\$25+\$40=\$100</math>. Since they decided to split their earnings equally among themselves, it follows that each person will get <math>\frac{\$100}{4}=\$25</math>. Since the friend who earned <math>\$40</math> will need to leave with <math>\$25</math>, he will have to give <math>\$40-\$25=\$15</math> to the others <math>\implies\boxed{\textbf{(C) }\$15}</math>.<br>
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https://www.youtube.com/watch?v=8hgK6rESdek&t=9s
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~ junaidmansuri
 
  
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==Solution 3==
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~NiuniuMaths
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Note that they will each get an equal amount, or the average, so we have <math>\dfrac{\$15+\$20+\$25+\$40}{4}=\dfrac{\$100}{4}=\$25,</math> and so the person with <math>\$40</math> will have to give <math>\$40-\$25=\boxed{\textbf{(C) }\$15}</math> to the others.
 
  
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[pog]
 
  
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==See also==  
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==Video Solution by Math-X (First understand the problem!!!)==
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https://youtu.be/UnVo6jZ3Wnk?si=UKNnVW0qEuIdyt8u&t=229
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~Math-X
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==Video Solution (🚀Just 1 min🚀)==
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https://youtu.be/CC5jRJ95QB0
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~Education, the Study of Everything
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==Video Solution by WhyMath==
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https://youtu.be/-mSgttsOv2Y
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~savannahsolver
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==Video Solution by The Learning Royal==
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https://youtu.be/eSxzI8P9_h8
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~The Learning Royal
 +
 
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==Video Solution by Interstigation==
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https://youtu.be/YnwkBZTv5Fw?t=62
 +
 
 +
~Interstigation
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==Video Solution by North America Math Contest Go Go Go==
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https://www.youtube.com/watch?v=ZwfPEYd55NQ
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~North America Math Contest Go Go Go
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==Video Solution by STEMbreezy==
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https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=37
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 +
~STEMbreezy
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==See Also==  
 
{{AMC8 box|year=2020|num-b=1|num-a=3}}
 
{{AMC8 box|year=2020|num-b=1|num-a=3}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 06:12, 24 January 2024

Problem

Four friends do yardwork for their neighbors over the weekend, earning $$15, $20, $25,$ and $$40,$ respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned $$40$ give to the others?

$\textbf{(A) }$5 \qquad \textbf{(B) }$10 \qquad \textbf{(C) }$15 \qquad \textbf{(D) }$20 \qquad \textbf{(E) }$25$

Solution

The friends earn $$\left(15+20+25+40\right)=$100$ in total. Since they decided to split their earnings equally, it follows that each person will get $$\left(\frac{100}{4}\right)=$25$. Since the friend who earned $$40$ will need to leave with $$25$, he will have to give $$\left(40-25\right)=\boxed{\textbf{(C) }$15}$ to the others.

Video Solution by NiuniuMaths (Easy to understand!)

https://www.youtube.com/watch?v=8hgK6rESdek&t=9s

~NiuniuMaths


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

https://youtu.be/UnVo6jZ3Wnk?si=UKNnVW0qEuIdyt8u&t=229

~Math-X

Video Solution (🚀Just 1 min🚀)

https://youtu.be/CC5jRJ95QB0

~Education, the Study of Everything

Video Solution by WhyMath

https://youtu.be/-mSgttsOv2Y

~savannahsolver

Video Solution by The Learning Royal

https://youtu.be/eSxzI8P9_h8

~The Learning Royal

Video Solution by Interstigation

https://youtu.be/YnwkBZTv5Fw?t=62

~Interstigation

Video Solution by North America Math Contest Go Go Go

https://www.youtube.com/watch?v=ZwfPEYd55NQ

~North America Math Contest Go Go Go

Video Solution by STEMbreezy

https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=37

~STEMbreezy

See Also

2020 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
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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