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

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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>
 
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>
 
~ junaidmansuri
 
~ junaidmansuri
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==Solution 3==
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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.
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-franzliszt
  
 
==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 12:00, 18 November 2020

Problem 5

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

To equally distribute to $5$ cups, we will simply divide $\dfrac{3}{4}$ by $5.$ Simplifying, we get: $\dfrac{3}{4} \cdot \dfrac{1}{5} = \dfrac{3}{20}.$ Converting that into a percent, we get an answer of $\boxed{\textbf{(C) }15}$

Solution 2

Assume that the pitcher has a total capacity of $100$ ounces. Since the pitcher is filled three fourths with pineapple juice, it follows that it contains $75$ ounces of pineapple juice. The pineapple juice is then divided equally into 5 cups, 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 $\implies\boxed{\textbf{(C) }15}$.
~ junaidmansuri

Solution 3

Notice that each cup receives $\frac 34 \cdot \frac 15=\frac{3}{20}=\frac{15}{100}$ of the entire pitcher which is $\textbf{(C) }15$ percent.

-franzliszt

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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