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 %

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Mathematics

28 July, 06:43

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 %

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Liberty Bishop · Answer 1

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