To find the correct proportion to determine the amount of orange juice, [tex]\(j\)[/tex], required to add to 18 liters of pineapple juice, we must consider the given ratio in the recipe, which is 2 parts orange juice to 8 parts pineapple juice.
Let's break this down step-by-step:
1. Understanding the Ratio:
The recipe states that for every 2 parts of orange juice, there are 8 parts of pineapple juice. This can be written as a ratio:
[tex]\[
\frac{2 \, \text{parts orange juice}}{8 \, \text{parts pineapple juice}}
\][/tex]
2. Setting Up the Proportion:
We need to maintain this ratio when we scale up the quantities. We are given 18 liters of pineapple juice and need to find the corresponding amount of orange juice, [tex]\(j\)[/tex], that maintains the same ratio. The proportion to find the amount of orange juice can be set up as follows:
[tex]\[
\frac{2 \, \text{parts orange juice}}{8 \, \text{parts pineapple juice}} = \frac{j \, \text{liters orange juice}}{18 \, \text{liters pineapple juice}}
\][/tex]
Simplifying, we get:
[tex]\[
\frac{2}{8} = \frac{j}{18}
\][/tex]
3. Conclusion:
The proportion we can use to find the amount of orange juice, [tex]\(j\)[/tex], that is needed to add to 18 liters of pineapple juice is:
[tex]\[
\frac{2}{8}=\frac{j}{18}
\][/tex]
Thus, the correct proportion is:
[tex]\[
\boxed{\frac{2}{8}=\frac{j}{18}}
\][/tex]
