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Difference between revisions of "2020 AMC 8 Problems/Problem 5"
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==Solution 2==
 
==Solution 2==
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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>
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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>
 
~jmansuri
 
~jmansuri
  

Revision as of 03:55, 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 $\implies\boxed{\textbf{(C) }15}$.
~jmansuri

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

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