Difference between revisions of "2020 AMC 8 Problems/Problem 1"
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| + | ==Problem== | ||
| + | Luka is making lemonade to sell at a school fundraiser. His recipe requires <math>4</math> times as much water as sugar and twice as much sugar as lemon juice. He uses <math>3</math> cups of lemon juice. How many cups of water does he need? | ||
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| + | <math>\textbf{(A) }6 \qquad \textbf{(B) }8 \qquad \textbf{(C) }12 \qquad \textbf{(D) }18 \qquad \textbf{(E) }24</math> | ||
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==Solution 1 (Direct)== | ==Solution 1 (Direct)== | ||
| − | + | We have <math>\text{water} : \text{sugar} : \text{lemon juice} = 4\cdot 2 : 2 : 1 = 8 : 2 : 1,</math> so Luka needs <math>3 \cdot 8 = \boxed{\textbf{(E) }24}</math> cups. | |
==Solution 2 (Stepwise)== | ==Solution 2 (Stepwise)== | ||
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Since the amount of water is <math>4</math> times the amount of sugar, he uses <math>6\cdot4=\boxed{\textbf{(E) }24}</math> cups of water. | Since the amount of water is <math>4</math> times the amount of sugar, he uses <math>6\cdot4=\boxed{\textbf{(E) }24}</math> cups of water. | ||
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~MRENTHUSIASM | ~MRENTHUSIASM | ||
Revision as of 16:48, 19 December 2021
Contents
Problem
Luka is making lemonade to sell at a school fundraiser. His recipe requires 
times as much water as sugar and twice as much sugar as lemon juice. He uses 
cups of lemon juice. How many cups of water does he need?
Solution 1 (Direct)
We have 
so Luka needs 
cups.
Solution 2 (Stepwise)
Since the amount of sugar is twice the amount of lemon juice, Luka uses 
cups of sugar.
Since the amount of water is times the amount of sugar, he uses 
cups of water.
~MRENTHUSIASM
Solution 3 (Combination of Solutions 1 and 2)
The ratio is 
or 
Since we know that Luka used 3 cups of lemon juice, he needs cups of sugar. Because the amount of water is times the amount of sugar Luka needs, he will need cups of water.
Thanks to MRENTHUSIASM for the inspiration!
EarthSaver 15:12, 11 June 2021 (EDT)
Video Solution by WhyMath
~savannahsolver
Video Solution
Video Solution by Interstigation
https://youtu.be/YnwkBZTv5Fw?t=34
~Interstigation
Video Solution by North America Math Contest Go Go Go
https://www.youtube.com/watch?v=f428YRwoXO4
~NAMCG
See also
| 2020 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 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. 
