Answer:
She should use 91 mL of the 60% solution (rounded to the nearest whole number).
Step-by-step explanation:
The first step to solve this question is to write the correct equations system. The two variables are :
[tex]X_{1}[/tex] : The amount of high concentration solution (60%) (in mL).
[tex]X_{2}[/tex] : The amount of low concentration solution (5%) (in mL).
The first equation for the mixing is :
[tex](0.60).X_{1}+(0.05).X_{2}=(0.15).(500)[/tex] (I)
Where [tex](0.60)[/tex] , [tex](0.05)[/tex] and [tex](0.15)[/tex] represent the percentages for [tex]X_{1}[/tex] , [tex]X_{2}[/tex] and the final 500 mL of copper-sulfate solution respectively.
The second equation is :
[tex]X_{1}+X_{2}=500[/tex] (II)
The equation (II) represents that the sum from the volumes of high and low concentration solution must be 500 mL.
The final step is to solve this equation system :
From (II) we find that :
[tex]X_{2}=500-X_{1}[/tex] (III)
If we use (III) in (I) :
[tex](0.60).X_{1}+(0.05).(500-X_{1})=(0.15).(500)[/tex]
[tex]0.60X_{1}+25-0.05X_{1}=75[/tex]
[tex]0.55X_{1}=50[/tex]
[tex]X_{1}=\frac{50}{0.55}=\frac{1000}{11}=90.9090[/tex] ≅ [tex]91[/tex]
She should use 91 mL of the 60% solution (rounded to the nearest whole number).
