2020 AMC 8 Problems/Problem 5

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?

$\textbf{(A) }5 \qquad \textbf{(B) }10 \qquad \textbf{(C) }15 \qquad \textbf{(D) }20 \qquad \textbf{(E) }25$

$\frac{3}{4}\div 5 = \frac{3}{4}\cdot\frac{1}{5} =\frac{3}{20} = \frac{3}{20} \cdot 100 = \textbf{(C) }15$

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

Solution 4

In the problem, it states that the pitcher is $\frac{3}{4}$ , or $75\%$ full. So, we can just divide this by $5$ to get $\frac{75\%}{5}=15\%$ , which means that the answer is $\boxed{\textbf{(C) }15}$ ~aaja3427 .

2020 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AJHSME/AMC 8 Problems and Solutions

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

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