how much water must be mixed with 5 pints of a solution that is 90% developer to produce a mixture that is 39% developer?

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The original solution contains 0.5 pints of water if 90% is developer.  Let x equal the number of pints of water that need to be added.  If 39% of the final mixture is developer, then 61% of it will be water.  The total amount of water (denoted x + 0.5) needs to equal 61% of the total number of pints of solution (which is 5 pints of original solution plus x pints of water).  That is, x + 0.5 = 0.61(x + 5).x + 0.5 = 0.61(x + 5)x + 0.5 = 0.61x + 3.05  0.39x = 2.55         x = 85/13 or approximately 6.54 pints of waterWe can check our answer:We originally have 4.5 pints of developer (that is 90% of 5 pints), and we now have 11.54 pints of the new solution (that is 5 pints of original solution plus 6.54 pints of water).  So, 4.5 pints of developer in 11.54 pints of solution is 4.5/11.54 = 39% developer.