Difference between revisions of "2020 AMC 8 Problems/Problem 5"

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==Solution 1==
 
==Solution 1==
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Each cup is filled with <math>\frac{3}{4} \cdot \frac{1}{5} = \frac{3}{20}</math> of the amount of juice in the pitcher, so the percentage is <math>\frac{3}{20} \cdot 100 = \boxed{\textbf{(C) }15}</math>.
 
Each cup is filled with <math>\frac{3}{4} \cdot \frac{1}{5} = \frac{3}{20}</math> of the amount of juice in the pitcher, so the percentage is <math>\frac{3}{20} \cdot 100 = \boxed{\textbf{(C) }15}</math>.
  
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==Solution 3==
 
==Solution 3==
 
Assume that the pitcher has a total capacity of <math>100</math> ounces. Since it is filled three fourths with pineapple juice, it contains <math>75</math> ounces of pineapple juice, which means that each cup will contain <math>\frac{75}{5}=15</math> ounces of pineapple juice. Since the total capacity of the pitcher was <math>100</math> ounces, it follows that each cup received <math>15\%</math> of the total capacity of the pitcher, yielding <math>\boxed{\textbf{(C) }15}</math> as the answer.
 
Assume that the pitcher has a total capacity of <math>100</math> ounces. Since it is filled three fourths with pineapple juice, it contains <math>75</math> ounces of pineapple juice, which means that each cup will contain <math>\frac{75}{5}=15</math> ounces of pineapple juice. Since the total capacity of the pitcher was <math>100</math> ounces, it follows that each cup received <math>15\%</math> of the total capacity of the pitcher, yielding <math>\boxed{\textbf{(C) }15}</math> as the answer.
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==Video Solution by North America Math Contest go go go==
 +
https://www.youtube.com/watch?v=bRzVP_caKrU
 +
~North America Math Contest go go go
 +
 +
==Video Solution==
 +
https://youtu.be/ph_qAhXXKP4
 +
 +
~savannahsolver
  
 
==Video Solution==
 
==Video Solution==
https://youtu.be/eSxzI8P9_h8
+
https://youtu.be/eSxzI8P9_h8 ~ The Learning Royal
 +
 
 +
==Video Solution by Interstigation==
 +
https://youtu.be/YnwkBZTv5Fw?t=165
 +
 
 +
~Interstigation
  
 
==See also==  
 
==See also==  
 
{{AMC8 box|year=2020|num-b=4|num-a=6}}
 
{{AMC8 box|year=2020|num-b=4|num-a=6}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 23:48, 19 October 2022

Problem

Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of $5$ cups. What percent of the total capacity of the pitcher did each cup receive?

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

Solution 1

Each cup is filled with $\frac{3}{4} \cdot \frac{1}{5} = \frac{3}{20}$ of the amount of juice in the pitcher, so the percentage is $\frac{3}{20} \cdot 100 = \boxed{\textbf{(C) }15}$.

Solution 2

The pitcher is $\frac{3}{4}$ full, i.e. $75\%$ full. Therefore each cup receives $\frac{75}{5}=\boxed{\textbf{(C) }15}$ percent of the total capacity.

Solution 3

Assume that the pitcher has a total capacity of $100$ ounces. Since it is filled three fourths with pineapple juice, it contains $75$ ounces of pineapple juice, which means that each cup will contain $\frac{75}{5}=15$ ounces of pineapple juice. Since the total capacity of the pitcher was $100$ ounces, it follows that each cup received $15\%$ of the total capacity of the pitcher, yielding $\boxed{\textbf{(C) }15}$ as the answer.

Video Solution by North America Math Contest go go go

https://www.youtube.com/watch?v=bRzVP_caKrU ~North America Math Contest go go go

Video Solution

https://youtu.be/ph_qAhXXKP4

~savannahsolver

Video Solution

https://youtu.be/eSxzI8P9_h8 ~ The Learning Royal

Video Solution by Interstigation

https://youtu.be/YnwkBZTv5Fw?t=165

~Interstigation

See also

2020 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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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