You work in a pharmacy that mixes different concentrations of saline solutions for its customers. The pharmacy has a supply of two concentrations, 0.50% and 2%. The function y equals StartFraction 100 left parenthesis 0.02 right parenthesis plus x left parenthesis 0.005 right parenthesis Over 100 plus x EndFraction gives the amount x in milliliters of the 0.5% solution you must add to 100 milliliters of the 2% solution to form a new concentration y of saline solution. How many milliliters of the 0.5% solution must you add for the combined solution to have a concentration of 0.79%
We begin with 100 mL of the 2% saline solution, and will add x mL of the 0.5% saline solution. The total volume of the mixture will be (100 + x) mL. The total mass of salt will be: (100)(2%) + (x)(0.5%) = 2 + 0.005x This would have to be 0.79% of the total volume: (100+x)(0.79%) = 0.79 + 0.0079x Equating: x = 417.24 mL
