SOLUTION: One canned juice drink is 25% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 20L that is 24% orange juice?
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Question 1102646: One canned juice drink is 25% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 20L that is 24% orange juice?
The fastest and easiest way to get the answer is with the method of alligation. (Do an internet search on that term if you want to learn more about the method.)
Here is how to solve the problem using my version of the method of alligation.
Think of three numbers on a number line: 5, 24, and 25 -- the percentages of the two ingredients and of the mixture.
The 24 is 19/20 of the way from 5 to 25 (25-5 = 20; 24-5 = 19).
That means 19/20 of the mixture must be the 25% juice.
To get 20L of the mixture, the amount of 25% juice you need is 19/20 of the total 20L, or 19L.
So you need to mix 19L of the 25% juice and 1L of the 5% juice to get 20L of 24% juice.
Here is the diagram that is used to find the answer using the formal method of alligation:
The two numbers in the top and bottom row of the first column are the percentages of the two ingredients.
The number in the middle row of the second column is the percentage of the mixture.
The numbers in the third column are the differences, found diagonally, between the numbers in the first column and the number in the middle column. (24-5 = 19; 25-24 = 1).
The two numbers in the third column tell you the ratio in which the two ingredients must be mixed.
