2020 AMC 8 Problems/Problem 1

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

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

Solution 2

Let $W, S,$ and $L$ represent the number of cups of water, sugar, and lemon juice that Luka needs for his recipe, respectively. We are given that $W=4S$ and $S=2L$ . Since $L=3$ , it follows that $S=6$ , which in turn implies that $W=24 \implies\boxed{\textbf{(E) }24}$ .
~jmansuri

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

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2020 AMC 8 Problems/Problem 1

Solution

Solution 2

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