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

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==Solution 1==
 
==Solution 1==
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>.
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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==
We have that <math>\text{lemonade} : \text{water} : \text{lemon juice} = 4\cdot 2 : 2 : 1 = 8 : 2 : 1</math>, so he needs <math>3 \cdot 8 = \boxed{\textbf{(E) }24}</math> cups.
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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.
  
 
==Video Solution==
 
==Video Solution==

Revision as of 10:50, 20 November 2020

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

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 Luka needs $3 \cdot 8 = \boxed{\textbf{(E) }24}$ cups.

Video Solution

https://youtu.be/FPC792h-mGE

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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