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The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe.

Lemon juice (mL)
Sugar (g)

Batch A
500
200

Batch B
750
300

Batch C
1500
600

Write an equation to describe the relationship between
j, the amount of lemon juice in milliliters, and
s, the amount of sugar in grams.

The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe. $\newline$ \begin{tabular}{lcc|} $\newline$ & Lemon juice (mL) & Sugar (g) \\ $\newline$ \hline Batch A & $500$ & $200$ \\ $\newline$ Batch B & $750$ & $300$ \\ $\newline$ Batch C & $1500$ & $600$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Write an equation to describe the relationship between $j$ , the amount of lemon juice in milliliters, and $s$ , the amount of sugar in grams.

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Write exponential functions: word problems

Full solution

Q. The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe.

\newline

\begin{tabular}{lcc|}

\newline

& Lemon juice (mL) & Sugar (g) \\

\newline

\hline Batch A &

500

&

200

\\

\newline

Batch B &

750

&

300

\\

\newline

Batch C &

1500

&

600

\\

\newline

\hline

\newline

\end{tabular}

\newline

Write an equation to describe the relationship between

j

, the amount of lemon juice in milliliters, and

s

, the amount of sugar in grams.

Observe Relationship: Observe the relationship between the amount of lemon juice and sugar in each batch. $\newline$ We can see that for Batch A, $500\,\text{mL}$ of lemon juice requires $200\,\text{g}$ of sugar. For Batch B, $750\,\text{mL}$ of lemon juice requires $300\,\text{g}$ of sugar. For Batch C, $1500\,\text{mL}$ of lemon juice requires $600\,\text{g}$ of sugar. We need to determine if there is a consistent ratio between the amount of lemon juice and sugar.
Calculate Ratios: Calculate the ratio of lemon juice to sugar for each batch. $\newline$ For Batch A, the ratio is $500\,\text{mL} / 200\,\text{g} = 2.5\,\text{mL/g}$ . $\newline$ For Batch B, the ratio is $750\,\text{mL} / 300\,\text{g} = 2.5\,\text{mL/g}$ . $\newline$ For Batch C, the ratio is $1500\,\text{mL} / 600\,\text{g} = 2.5\,\text{mL/g}$ . $\newline$ Since the ratio is consistent across all batches, we can use this ratio to write the equation.
Write Equation: Write the equation using the consistent ratio. $\newline$ Since the ratio of lemon juice to sugar is $2.5\,\text{mL/g}$ , we can write the equation as: $\newline$ $j = 2.5 \times s$ $\newline$ This equation shows that for every gram of sugar, we need $2.5$ milliliters of lemon juice.

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