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?
 
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>
 
<math>\textbf{(A) }6 \qquad \textbf{(B) }8 \qquad \textbf{(C) }12 \qquad \textbf{(D) }18 \qquad \textbf{(E) }24</math>
  
==Solution 1==
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==Solution==
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==
 
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>
 
~[http://artofproblemsolving.com/community/user/jmansuri junaidmansuri]
 
 
 
==Solution 3==
 
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]
 
 
 
==Solution 4==
 
 
 
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} 24</math>.
 
 
 
-franzliszt
 
 
 
==Solution 5==
 
 
 
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>
 
 
 
~ bsu1
 
  
 
==Video Solution==
 
==Video Solution==
https://youtu.be/FPC792h-mGE
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https://youtu.be/eSxzI8P9_h8
 
 
~savannahsolver
 
  
 
==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}}
we just get 4*3*2=24$ which is E
 
-oceanxia
 

Revision as of 00:20, 10 January 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

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.

Video Solution

https://youtu.be/eSxzI8P9_h8

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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