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

Revision as of 07:10, 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 he needs $3 \cdot 8 = \boxed{\textbf{(E) }24}$ cups.

Video Solution

https://youtu.be/FPC792h-mGE

2020 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Revision as of 06:58, 20 November 2020 (view source) Sevenoptimus (talk \| contribs) m (Fixed wording) ← Older edit		Revision as of 07:10, 20 November 2020 (view source) Sevenoptimus (talk \| contribs) m (Fixed page styling) Newer edit →
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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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