SOLUTION: Evan wants to combine two fruit drinks to get 50 liters of a drink that will be 8% sugar. Drink A is 4% sugar and drink B is 9% sugar. How much of each drink should he use?

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Question 1106577: Evan wants to combine two fruit drinks to get 50 liters of a drink that will be 8% sugar. Drink A is 4% sugar and drink B is 9% sugar. How much of each drink should he use?
Found 2 solutions by stanbon, greenestamps:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Evan wants to combine two fruit drinks to get 50 liters of a drink that will be 8% sugar. Drink A is 4% sugar and drink B is 9% sugar. How much of each drink should he use?
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Quantity Eq:: A + B = 50 liters
Sugar Eq:::: 4A + 9B = 8(A + B)
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Modify for elimination::
A + B = 50
4A - B = 0
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Add and solve for "B"::
5A = 50
A = 10 liters (amt. of drink A needed)
B = 50-A = 40 liters (amt. of drink B needed)
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Cheers,
Stan H.
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Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The desired 8% is 4 times as close to 9% as it is to 4%. (9-8=1; 8-4=4.)

That means the mixture must have 4 times as much of the 9% ingredient as the 4% ingredient.

A 4:1 ratio with a total volume of 50 liters means 40 liters of drink B and 10 liters of drink A.

Here is how this answer is obtained formally, using the process of alligation. (Not a familiar word; spell checker doesn't even recognize it. Look around on the internet to learn more about the method.)

matrix%283%2C3%2C4%2C%22%22%2C1%2C%22%22%2C8%2C%22%22%2C9%2C%22%22%2C4%29

The numbers in the first column are the percentages of the two ingredients, 4% and 9%; the number in the middle column is the percentage of the mixture, 8%.

The numbers in the third column are the differences, calculated diagonally, between the numbers in the first two columns: 9-8=1 and 8-4=4.

When the calculations are done this way, the numbers in the third column show the ratio in which the two ingredients must be mixed: 4 parts of the 9% ingredient to 1 part of the 4% ingredient.