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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 1

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 $W=24 \implies\boxed{\textbf{(E) }24}$.
~junaidmansuri

Solution 3

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

[pog]

Solution 4

We are given that $4w:s$ and $2s=l$ which we combine to get $8w:2s:l$. Letting all the variables equal $3$, we find that the answer is $3\cdot 8=\textbf{(E)}\ 24$.

-franzliszt

Solution 5

Put the numbers in ratios $4w:s$ and $2s:lj$ when w = water, s = sugar, and lj = lemon juice. then since we know there is $3$ cups of lemon juice, do the math. $3\cdot2\cdot4=6\cdot4=24$

~ bsu1

Video Solution

~savannahsolver

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