Concentration Word Problem
My husband made 1/2 gallon of orange juice by mixing two containers of water with one container of frozen juice concentrate. I like orange juice that is precisely 18% juice concentrate and 82% water. How many ounces of my husbands mixture and how much water should i use to create one cup of juice that I will like?
In the husbands mix you have 1/3 of the total volume as juice.So it has 1/3*100% = 33.33% of juice. So we need to add more water to lower the concentration to 18%.
At the moment;
Volume of the mix = 1/2 gal.
Volume % of juice = 33.33%
Let us consider the volume of a cup is 8 ounces(U.S. customary).
So in the final mix of your desire will have;
18/100*8 = 1.44 ounce of juice and 82/100*8 = 6.56 ounces of water.
For your mix juice only comes from the husbands mix. so 1.44 ounces comes from husbands mix. In that mix we have 33.33% of juice. So 33.33% represent 1.44 ounces.
The volume taken by husbands mix = 100/33.33*1.44 = 4.32 ounces.
From these 4.32 ounces 1.44 is juice and rest is water.
So the water from juice mix = 4.32-1.44 = 2.88
In your desired mix you have 6.56 of water. 2.88 comes from the juice mix and the rest is coming from the water you add separately.
The water added last = 6.56-2.88 = 3.68
So finally to make your dream cup of juice you need to add 4.32 ounces of juice mix from your husbands mixture and 3.68 ounces of water.