A fruit juice recipe calls for 5 parts orange juice and 6 parts pineapple juice. Which proportion can be used to find the amount of orange juice, [tex]$j$[/tex], that is needed to add to 21 L of pineapple juice?
[tex]\frac{30}{21}=\frac{j}{100}[/tex]
[tex]\frac{6}{5}=\frac{j}{21}[/tex]
[tex]\frac{6}{j}=\frac{5}{21}[/tex]
[tex]\frac{5}{6}=\frac{j}{21}[/tex]
Answer (2)
The correct proportion to find the amount of orange juice needed for 21 L of pineapple juice is 6 5 = 21 j . This maintains the ratio from the original recipe of orange juice to pineapple juice. The selected option is 6 5 = 21 j .
;
The problem requires finding the correct proportion to determine the amount of orange juice needed for 21 L of pineapple juice, given a recipe with a 5:6 ratio of orange juice to pineapple juice.
Set up the ratio of orange juice to pineapple juice as 6 5 .
Form the proportion 6 5 = 21 j , where j represents the amount of orange juice needed.
The correct proportion is 6 5 = 21 j .
Explanation
Understanding the Problem We are given a recipe that calls for 5 parts orange juice and 6 parts pineapple juice. We need to find the correct proportion to determine the amount of orange juice, denoted as j , required when using 21 L of pineapple juice.
Setting up the Ratio The recipe specifies a ratio of 5 parts orange juice to 6 parts pineapple juice. This can be written as a fraction: pineapple juice orange juice = 6 5
Forming the Proportion We are given that we have 21 L of pineapple juice. We need to find the amount of orange juice, j , that corresponds to this amount. We can set up a proportion: 6 5 = 21 j This proportion states that the ratio of orange juice to pineapple juice should be the same as the ratio of 5 to 6.
Identifying the Correct Proportion Now, let's compare this proportion with the given options:
21 30 = 100 j : This is incorrect because it doesn't relate the orange juice to pineapple juice ratio.
5 6 = 21 j : This is incorrect because it inverts the ratio of orange juice to pineapple juice.
j 6 = 21 5 : This is incorrect because it also inverts the ratio and mixes the quantities.
6 5 = 21 j : This is the correct proportion as it matches our derived proportion.
Final Answer Therefore, the correct proportion to find the amount of orange juice needed is: 6 5 = 21 j
Examples
Imagine you're baking a cake and the recipe calls for a specific ratio of flour to sugar. If you want to make a larger cake, you need to maintain the same ratio to ensure the cake turns out perfectly. Similarly, in this problem, we're scaling up the fruit juice recipe while keeping the ratio of orange juice to pineapple juice consistent. This concept of proportions is widely used in cooking, construction, and many other fields where maintaining consistent ratios is crucial for success.
