SOLUTION: Need to find the average of a percentage based on other variables: I have 1 cup of apple juice that is 50% apple juice. I want to add 2 more cups of apple juice to the 1 cup,

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Question 93548: Need to find the average of a percentage based on other variables:
I have 1 cup of apple juice that is 50% apple juice.
I want to add 2 more cups of apple juice to the 1 cup, but it is 75% apple juice.
What is the average percent of apple juice when I add it to the 1 cup
a=1 cup
(a's percentage) a1=50%
b=3 cups
(b's percentage) b1=75%
IF a=b then you would add a1 + b1 then divide by 2 (62.5%)
if a1=b1 then the percent of apple juice would be the same
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
I have 1 cup of apple juice that is 50% apple juice.
I want to add 2 more cups of apple juice to the 1 cup, but it is 75% apple juice.
What is the average percent of apple juice when I add it to the 1 cup
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50% juice DATA:
Amount = 1 cup ; amt of active ingredient = 0.5 cup
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75% juice DATA;
Amount = 2 cups ; amt of active ingredient = (3/4)*2 = 1.5 cup
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Mixture DATA where % is unknown:
Amount = 3 cups ; amt of active ingredient = 3x
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EQUATION:
active + active = active
0.5 + 1.5 = 3x
2 = 3x
x = 2/3 or 66.67 %
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You end up with a 66.67% mixture.
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cheers,
Stan H.