2020 AMC 8 Problems/Problem 5: Difference between revisions
Khizarrouf (talk | contribs) No edit summary |
|||
| (20 intermediate revisions by 14 users not shown) | |||
| Line 5: | Line 5: | ||
==Solution 1== | ==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>. | 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>. | ||
| Line 13: | Line 14: | ||
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. | ||
==Video Solution== | ==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 | https://www.youtube.com/watch?v=bRzVP_caKrU | ||
~North America Math Contest go go go | ~North America Math Contest go go go | ||
==Video Solution== | ==Video Solution by WhyMath== | ||
https://youtu.be/ph_qAhXXKP4 | https://youtu.be/ph_qAhXXKP4 | ||
| Line 23: | Line 39: | ||
==Video Solution== | ==Video Solution== | ||
https://youtu.be/eSxzI8P9_h8 | https://youtu.be/eSxzI8P9_h8 ~ The Learning Royal | ||
==Video Solution by Interstigation== | ==Video Solution by Interstigation== | ||
| Line 29: | Line 45: | ||
~Interstigation | ~Interstigation | ||
==Video Solution by STEMbreezy== | |||
https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=205 | |||
~STEMbreezy | |||
== Video solution by TheNeuralMathAcademy == | |||
https://youtu.be/mGQw1yALXYM&t=431s | |||
==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}} | ||
[[Category:Introductory Algebra Problems]] | |||
Latest revision as of 23:47, 20 August 2025
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 
cups. What percent of the total capacity of the pitcher did each cup receive?
Solution 1
Each cup is filled with 
of the amount of juice in the pitcher, so the percentage is 
.
Solution 2
The pitcher is 
full, i.e. 
full. Therefore each cup receives 
percent of the total capacity.
Solution 3
Assume that the pitcher has a total capacity of 
ounces. Since it is filled three fourths with pineapple juice, it contains 
ounces of pineapple juice, which means that each cup will contain 
ounces of pineapple juice. Since the total capacity of the pitcher was ounces, it follows that each cup received 
of the total capacity of the pitcher, yielding 
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🚀)
~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
~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
Video solution by TheNeuralMathAcademy
https://youtu.be/mGQw1yALXYM&t=431s
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
