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

(Solution 5)
(Video Solution by Interstigation)
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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?
 
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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==Solution 1==
 
==Solution 1==
Luka will need <math>3\cdot 2=6</math> cups of sugar and <math>6\cdot 4=24</math> cups of water. The answer is <math>\boxed{\textbf{(E) } 24}</math>.
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We have that <math>\text{lemonade} : \text{water} : \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==
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==Solution 2 (Stepwise)==
Let <math>W, S,</math> and <math>L</math> represent the number of cups of water, sugar, and lemon juice that Luka needs for his recipe, respectively. We are given that <math>W=4S</math> and <math>S=2L</math>. Since <math>L=3</math>, it follows that <math>S=6</math>, which in turn implies that <math>W=24 \implies\boxed{\textbf{(E) }24}</math>.<br>
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Since the amount of sugar is twice the amount of lemon juice, Luka uses <math>3\cdot2=6</math> cups of sugar.
~ junaidmansuri
 
  
==Solution 3==
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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.
We have that <math>\textsf{lemonade} : \textsf{water} : \textsf{lemon juice} = 8 : 2 : 1,</math> so we have <math>3 \cdot 8 = \boxed{\textbf{(E) }24}.</math>
 
  
[pog]
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~MRENTHUSIASM
  
==Solution 4==
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==Video Solution by WhyMath==
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https://youtu.be/FPC792h-mGE
  
We are given that <math>4w:s</math> and <math>2s=l</math> which we combine to get <math>8w:2s:l</math>. Letting all the variables equal <math>3</math>, we find that the answer is <math>3\cdot 8=\textbf{(E)}\ 24</math>.
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~savannahsolver
  
-franzliszt
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==Video Solution==
==Solution 5==
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https://youtu.be/eSxzI8P9_h8
  
Put the numbers in ratios <math>4w:s</math> and <math>2s:lj</math> when w = water, s = sugar, and lj = lemon juice. then since we know there is <math>3</math> cups of lemon juice, do the math. <math>3\cdot2\cdot4=6\cdot4=24</math>
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==Video Solution by Interstigation==
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https://youtu.be/YnwkBZTv5Fw?t=34
  
 
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~Interstigation
~ bsu1
 
  
 
==See also==
 
==See also==
{{AMC8 box|year=2020|before=First problem|num-a=2}}
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{{AMC8 box|year=2020|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 14:22, 18 April 2021

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

We have that $\text{lemonade} : \text{water} : \text{lemon juice} = 4\cdot 2 : 2 : 1 = 8 : 2 : 1$, 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

Video Solution by WhyMath

https://youtu.be/FPC792h-mGE

~savannahsolver

Video Solution

https://youtu.be/eSxzI8P9_h8

Video Solution by Interstigation

https://youtu.be/YnwkBZTv5Fw?t=34

~Interstigation

See also

2020 AMC 8 (ProblemsAnswer KeyResources)
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

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