SOLUTION: A cup that is filled with equal parts red, green, and blue dye spills half of its contents. Enough green dye is then poured into the cup to fill it up again. what is the ratio of

Question 408667: A cup that is filled with equal parts red, green, and blue dye spills half of its contents. Enough green dye is then poured into the cup to fill it up again. what is the ratio of red to green to blue dye now?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Assume that the mixture is thoroughly mixed, and that initially the ratio of red to green to blue dye is 1 :1:1.
Let x = weight of each of the red, green, and blue dye.
==> total weight of mixture is 3x.
After half of the mixture was spilled, there remains 3x/2 of the mixture.
This was also the weight of the green dye that was put into the mixture after the spill.
Also, after the spill, the weight of each dye is x/2.
Then the new weight of the green dye is 3x/2 + x/2 = 2x.
The weight of each of the red and blue dye is still x/2.
Hence the ratio of red to green to blue dye is 1/2: 2: 1/2, or 1:4:1.
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