SOLUTION: A 90% dye solution is to be mixed with 75% dye solution to get 120 liters of a 78% dye solution. How many liters of the 90% and 75% solution will be needed. I know the short cut to

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Question 823376: A 90% dye solution is to be mixed with 75% dye solution to get 120 liters of a 78% dye solution. How many liters of the 90% and 75% solution will be needed. I know the short cut to get answer but I don't know how to break equation down step by step.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
{Amount of dye}/{Amount of solution}={concentration}

Let u = how much volume of the 90%
Let v = how much volume of the 75%

Amount of dye: u%2A90%2Bv%2A75, being 100 times larger than actual

Amount of dye solution: u%2Bv=120, which is also one of your system equations.

The other system equation is %2890u%2B75v%29%2F120=78, which is based directly on the first expression explained.