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

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==Solution 1==
 
==Solution 1==
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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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Luka will need <math>3\cdot 2=6</math> cups of sugar and thus <math>6\cdot 4=24</math> cups of water. The answer is <math>\boxed{\textbf{(E) } 24}</math>.
  
 
==Solution 2==
 
==Solution 2==
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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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We have that <math>\text{lemonade} : \text{water} : \text{lemon juice} = 4\cdot 2 : 2 : 1 = 8 : 2 : 1</math>, so we have <math>3 \cdot 8 = \boxed{\textbf{(E) }24}.</math>
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~[http://artofproblemsolving.com/community/user/jmansuri junaidmansuri]
 
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==Solution 3==
 
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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>
 
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[pog]
 
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==Solution 4==
 
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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=\boxed{\textbf{(E) }24} </math>.
 
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-franzliszt
 
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==Solution 5==
 
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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=\boxed{\textbf{(E) }24}.</math>
 
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~ bsu1
 
  
 
==Video Solution==
 
==Video Solution==
 
https://youtu.be/FPC792h-mGE
 
https://youtu.be/FPC792h-mGE
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~savannahsolver
 
  
 
==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}}
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we just get 4*3*2=24$ which is E
 
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-oceanxia
 

Revision as of 05:51, 20 November 2020

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

Luka will need $3\cdot 2=6$ cups of sugar and thus $6\cdot 4=24$ cups of water. The answer is $\boxed{\textbf{(E) } 24}$.

Solution 2

We have that $\text{lemonade} : \text{water} : \text{lemon juice} = 4\cdot 2 : 2 : 1 = 8 : 2 : 1$, so we have $3 \cdot 8 = \boxed{\textbf{(E) }24}.$

Video Solution

https://youtu.be/FPC792h-mGE

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC Logo.png

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