During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

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

(Removed solutions that are effectively the same as each other, fixed grammar, and improved clarity)
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==
<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>
+
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 answer is <math>\frac{3}{20} \cdot 100 = \boxed{\textbf{(C) }15}</math>.
 
 
==Solution==
 
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==
 
==Solution 2==
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>
+
The pitcher is <math>\frac{3}{4}</math> full, i.e. <math>75\%</math> full. Therefore each cup receives <math>\frac{75\%}{5}=15\%</math> of the total capacity, so the answer is <math>\boxed{\textbf{(C) }15}</math>.
~[http://artofproblemsolving.com/community/user/jmansuri junaidmansuri]
 
  
 
==Solution 3==
 
==Solution 3==
Notice that each cup receives <math>\frac 34 \cdot \frac 15=\frac{3}{20}=\frac{15}{100}</math>
+
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>
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
 
  
==Solution 4==
 
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==
 
==Video Solution==
 
https://youtu.be/ph_qAhXXKP4
 
https://youtu.be/ph_qAhXXKP4
 
~savannahsolver
 
  
 
==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 06:15, 20 November 2020

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 answer 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 $\frac{75\%}{5}=15\%$ of the total capacity, so the answer is $\boxed{\textbf{(C) }15}$.

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 $\boxed{\textbf{(C) }15}$

Video Solution

https://youtu.be/ph_qAhXXKP4

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

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

Invalid username
Login to AoPS