Difference between revisions of "2020 AMC 8 Problems/Problem 1"

Latest revision as of 06:06, 24 January 2024

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 $4$ times as much water as sugar and twice as much sugar as lemon juice. He uses $3$ cups of lemon juice. How many cups of water does he need?

$\textbf{(A) }6 \qquad \textbf{(B) }8 \qquad \textbf{(C) }12 \qquad \textbf{(D) }18 \qquad \textbf{(E) }24$

Solution 1 (Direct)

We have $\text{water} : \text{sugar} : \text{lemon juice} = 4\cdot 2 : 2 : 1 = 8 : 2 : 1,$ so Luka needs $3 \cdot 8 = \boxed{\textbf{(E) }24}$ cups.

Solution 2 (Stepwise)

Since the amount of sugar is twice the amount of lemon juice, Luka uses $3\cdot2=6$ cups of sugar.

Since the amount of water is $4$ times the amount of sugar, he uses $6\cdot4=\boxed{\textbf{(E) }24}$ cups of water.

~MRENTHUSIASM

Solution 3 (Combination of Solutions 1 and 2)

The ratio is $\text{Water}:\text{Sugar}:\text{Lemon Juice},$ or $8:2:1.$ Since we know that Luka used 3 cups of lemon juice, he needs $3\cdot2=6$ cups of sugar. Because the amount of water is $4$ times the amount of sugar Luka needs, he will need $6\cdot4=\boxed{\textbf{(E) }24}$ 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🚀)

https://youtu.be/T1K8irAOxRk

~Education, the Study of Everything

Video Solution by WhyMath

https://youtu.be/FPC792h-mGE

~savannahsolver

Video Solution by The Learning Royal

https://youtu.be/eSxzI8P9_h8

~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

@@ Line 1: / Line 1: @@
 ==Problem==
-Luka is making sussy juice to sell at a school fundraiser. His recipe requires <math>4</math> times as much pee as diarrhea and twice as much diarrhea as liquid fart. He uses <math>3</math> cups of liquid fart. How many cups of pee does he need?
+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?
 <math>\textbf{(A) }6 \qquad \textbf{(B) }8 \qquad \textbf{(C) }12 \qquad \textbf{(D) }18 \qquad \textbf{(E) }24</math>
@@ Line 20: / Line 20: @@
 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🚀)==

2020 AMC 8 (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
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All AJHSME/AMC 8 Problems and Solutions

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