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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 0.87​%?

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sqdancefan

Answer:

  305.4 mL

Step-by-step explanation:

You want to solve for x when y = 0.0087 in the equation ...

  [tex]y = \dfrac{100(0.02)+x(0.005)}{100+x}[/tex]

Volume

Solving the equation for x, we have ...

  [tex]y(100+x)=2+0.005x\qquad\text{multiply by 100+x}\\\\x(y-0.005)=2-100y\qquad\text{isolate x terms}\\\\x=\dfrac{2-100y}{y-0.005}\qquad\text{divide by x coefficient}[/tex]

Using the given value for y, this is ...

  [tex]x=\dfrac{2-100(0.0087)}{0.0087-0.005}=\dfrac{1.13}{0.0037}=305.\overline{405}[/tex]

About 305.4 mL of the 0.5% solution must be added.

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