SOLUTION: when you have a recipe of 5 cups of concentrate and 8 cups of water how do you arrive at the answer for how much of each product you need for one full cup of juice

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Question 929596: when you have a recipe of 5 cups of concentrate and 8 cups of water how do you arrive at the answer for how much of each product you need for one full cup of juice
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F8+=+x%2F%281-x%29 where x is the fraction of 1 cup
Do cross products
8x+=+5%281-x%29+
8x+=+5+-+5x
add 5x to each side
13x = 5
divide each side by 13
x = 5/13 cup
%281-x%29+=%281+-+5%2F13%29
1-x = 8/13 cup
So we need a mixture of 5/13 concentrate with 8/13 water
If we want ounces we need 8*(5/13) with 8*(8/13)
or 40/13 ounces with 64/13 ounces
or 3.077 ounces with 4.92 ounces