Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2020 AMC 8 Problems/Problem 5"
m (→‎Solution 1: fix latex)
 
(29 intermediate revisions by 19 users not shown)
Line 1: Line 1:
−
==Problem 5==
+
==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 <math>5</math> cups. What percent of the total capacity of the pitcher did each cup receive?
 
Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of <math>5</math> cups. What percent of the total capacity of the pitcher did each cup receive?
  
 
<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 1==
 +
 +
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>.
  
−
<math>\frac{3}{4}\div 5 = \frac{3}{4}\cdot\frac{1}{5} =\frac{3}{20} = \frac{3}{20} \cdot 100 = \textbf{(C) }15</math>
+
==Solution 2==
 +
The pitcher is <math>\frac{3}{4}</math> full, i.e. <math>75\%</math> full. Therefore each cup receives <math>\frac{75}{5}=\boxed{\textbf{(C) }15}</math> percent of the total capacity.
 +
 
 +
==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.
 +
 
 +
==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=dBVy_7cb8HQGTdBs&t=433
  
−
==Solution==
+
~Math-X
−
To equally distribute to <math>5</math> cups, we will simply divide <math>\dfrac{3}{4}</math> by <math>5.</math> Simplifying, we get: <math>\dfrac{3}{4} \cdot \dfrac{1}{5} = \dfrac{3}{20}.</math> Converting that into a percent, we get an answer of <math>\boxed{\textbf{(C) }15}</math>
 
  
−
==Solution 2==
+
==Video Solution (🚀Very Fast🚀)==
−
Assume that the pitcher has a total capacity of <math>100</math> ounces. Since the pitcher is filled three fourths with pineapple juice, it follows that it contains <math>75</math> ounces of pineapple juice. The pineapple juice is then divided equally into 5 cups, 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 <math>\implies\boxed{\textbf{(C) }15}</math>.<br>
+
https://youtu.be/_6cEquyjWXQ
−
~[http://artofproblemsolving.com/community/user/jmansuri junaidmansuri]
 
  
−
==Solution 3==
+
~Education, the Study of Everything
−
Notice that each cup receives <math>\frac 34 \cdot \frac 15=\frac{3}{20}=\frac{15}{100}</math>
 
−
Notice that each cup receives <math>\frac 34 \cdot \frac 15=\frac{3}{20}=\frac{15}{100}</math> of the entire pitcher which is <math>\textbf{(C) }15</math> percent.
 
  
−
-franzliszt
+
==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
  
−
==Solution 4==
+
==Video Solution by WhyMath==
−
In the problem, it states that the pitcher is <math>\frac{3}{4}</math>, or <math>75\%</math> full. So, we can just divide this by <math>5</math> to get <math>\frac{75\%}{5}=15\%</math>, which means that the answer is <math>\boxed{\textbf{(C) }15}</math>
 
−
~aaja3427
 
−
.
 
−
==Video Solution==
 
 
https://youtu.be/ph_qAhXXKP4
 
https://youtu.be/ph_qAhXXKP4
  
 
~savannahsolver
 
~savannahsolver
 +
 +
==Video Solution==
 +
https://youtu.be/eSxzI8P9_h8 ~ The Learning Royal
 +
 +
==Video Solution by Interstigation==
 +
https://youtu.be/YnwkBZTv5Fw?t=165
 +
 +
~Interstigation
 +
 +
==Video Solution by STEMbreezy==
 +
https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=205
 +
 +
~STEMbreezy
  
 
==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}}

Latest revision as of 12:39, 6 June 2024

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 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=dBVy_7cb8HQGTdBs&t=433

~Math-X

Video Solution (🚀Very Fast🚀)

https://youtu.be/_6cEquyjWXQ

~Education, the Study of Everything

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 by WhyMath

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

Video Solution by STEMbreezy

https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=205

~STEMbreezy

See also

2020 AMC 8 (Problems • Answer Key • Resources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2020_AMC_8_Problems/Problem_5&oldid=220152"