To solve the problem correctly, let's ensure we understand the necessary proportions for the juice mixture and verify if any provided choices match this proportion.
1. According to the recipe, the correct proportion is 2 parts orange juice to 13 parts pineapple juice (as you need to figure out the proportion with 13 liters of pineapple juice).
We will go through each given choice to see if any satisfy the same proportional relationship:
First choice: [tex]\(\frac{2}{8} = \frac{1}{10}\)[/tex]
- Cross-multiplication: [tex]\(2 \times 10 = 8 \times 1\)[/tex]
- [tex]\(20 \neq 8\)[/tex]
- This proportion does not hold true.
Second choice: [tex]\(\frac{8}{2} = \frac{1}{18}\)[/tex]
- Cross-multiplication: [tex]\(8 \times 18 = 2 \times 1\)[/tex]
- [tex]\(144 \neq 2\)[/tex]
- This proportion does not hold true.
Third choice: [tex]\(\frac{6}{1} = \frac{2}{18}\)[/tex]
- Cross-multiplication: [tex]\(6 \times 18 = 1 \times 2\)[/tex]
- [tex]\(108 \neq 2\)[/tex]
- This proportion does not hold true.
Fourth choice: [tex]\(\frac{16}{18} = \frac{1}{100}\)[/tex]
- Cross-multiplication: [tex]\(16 \times 100 = 18 \times 1\)[/tex]
- [tex]\(1600 \neq 18\)[/tex]
- This proportion does not hold true.
Upon examining all the provided choices, we see that none of them correctly reflect the proportion [tex]\(2 \text{ parts orange juice} : 13 \text{ parts pineapple juice}\)[/tex].
Therefore, there is no correct match in the provided choices for the required proportion.
