Difference between revisions of "2020 AMC 8 Problems/Problem 1"
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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> | <math>\textbf{(A) }6 \qquad \textbf{(B) }8 \qquad \textbf{(C) }12 \qquad \textbf{(D) }18 \qquad \textbf{(E) }24</math> | ||
| − | ==Solution 1== | + | ==Solution 1 (Direct)== |
| − | We have | + | 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)== | ||
| Line 14: | Line 14: | ||
~MRENTHUSIASM | ~MRENTHUSIASM | ||
| − | ==Solution 3== | + | ==Solution 3 (Combination of Solutions 1 and 2)== |
| − | The ratio is Water:Sugar:Lemon | + | The ratio is <math>\text{Water}:\text{Sugar}:\text{Lemon Juice},</math> or <math>8:2:1.</math> Since we know that Luka used 3 cups of lemon juice, he needs <math>3\cdot2=6</math> cups of sugar. Because the amount of water is <math>4</math> times the amount of sugar Luka needs, he will need <math>6\cdot4=\boxed{\textbf{(E) }24}</math> cups of water. |
| − | Thanks to | + | Thanks to MRENTHUSIASM for the inspiration! |
| − | ~ | + | EarthSaver 15:12, 11 June 2021 (EDT) |
| + | |||
| + | ==Video Solution by NiuniuMaths (Easy to understand!)== | ||
| + | https://www.youtube.com/watch?v=8hgK6rESdek&t=9s | ||
| + | |||
| + | ~NiuniuMaths | ||
| + | |||
| + | ==Video Solution by Math-X (First understand the problem!!!)== | ||
| + | https://youtu.be/UnVo6jZ3Wnk?si=KUWl6TL6PU9LtC7o&t=105 | ||
| + | |||
| + | ~Math-X | ||
| + | |||
| + | ==Video Solution (🚀Under 1 min🚀)== | ||
| + | https://youtu.be/T1K8irAOxRk | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==Video Solution by WhyMath== | ==Video Solution by WhyMath== | ||
| Line 26: | Line 41: | ||
~savannahsolver | ~savannahsolver | ||
| − | ==Video Solution== | + | ==Video Solution by The Learning Royal== |
https://youtu.be/eSxzI8P9_h8 | https://youtu.be/eSxzI8P9_h8 | ||
| + | |||
| + | ~The Learning Royal | ||
==Video Solution by Interstigation== | ==Video Solution by Interstigation== | ||
| Line 33: | Line 50: | ||
~Interstigation | ~Interstigation | ||
| + | |||
| + | ==Video Solution by North America Math Contest Go Go Go== | ||
| + | https://www.youtube.com/watch?v=f428YRwoXO4 | ||
| + | |||
| + | ~North America Math Contest Go Go Go | ||
| + | |||
| + | ==Video Solution by STEMbreezy== | ||
| + | https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS | ||
| + | |||
| + | ~STEMbreezy | ||
==See also== | ==See also== | ||
{{AMC8 box|year=2020|before=First Problem|num-a=2}} | {{AMC8 box|year=2020|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 06:06, 24 January 2024
Contents
- 1 Problem
- 2 Solution 1 (Direct)
- 3 Solution 2 (Stepwise)
- 4 Solution 3 (Combination of Solutions 1 and 2)
- 5 Video Solution by NiuniuMaths (Easy to understand!)
- 6 Video Solution by Math-X (First understand the problem!!!)
- 7 Video Solution (🚀Under 1 min🚀)
- 8 Video Solution by WhyMath
- 9 Video Solution by The Learning Royal
- 10 Video Solution by Interstigation
- 11 Video Solution by North America Math Contest Go Go Go
- 12 Video Solution by STEMbreezy
- 13 See also
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 NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=8hgK6rESdek&t=9s
~NiuniuMaths
Video Solution by Math-X (First understand the problem!!!)
https://youtu.be/UnVo6jZ3Wnk?si=KUWl6TL6PU9LtC7o&t=105
~Math-X
Video Solution (🚀Under 1 min🚀)
~Education, the Study of Everything
Video Solution by WhyMath
~savannahsolver
Video Solution by The Learning Royal
~The Learning Royal
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
~North America Math Contest Go Go Go
Video Solution by STEMbreezy
https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS
~STEMbreezy
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. 
