Difference between revisions of "2020 AMC 8 Problems/Problem 5"
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| − | ==Problem | + | ==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> | + | 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>. |
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==Solution 2== | ==Solution 2== | ||
| − | + | 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>. | |
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==Solution 3== | ==Solution 3== | ||
| − | + | 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> | |
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==Video Solution== | ==Video Solution== | ||
https://youtu.be/ph_qAhXXKP4 | https://youtu.be/ph_qAhXXKP4 | ||
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==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 
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 answer is 
.
Solution 2
The pitcher is 
full, i.e. 
full. Therefore each cup receives 
of the total capacity, so the answer is 
.
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
Video Solution
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
