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A pharmacist wishes to strengthen a mixture from 10%alcohol to 30% alcohol. How much pure alcohol should be added to 7 liters of the 10% mixture?

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danialamin

Answer:

2 litres of pure alcohol will be added to make the overall concentration of 9 litres of mixture as 30%.

Explanation:

Suppose x is the number of litres added to the 10% mixture than the quantity of new mixture is given as below

  • [tex]n_{old}=7[/tex] litres
  • [tex]n_{new}=7+x[/tex] litres

Also the quantity of alcohol is given as

  • [tex]q_{old}=10 \% \, of \, 7 \, litres =0.7[/tex]
  • [tex]q_{added}=x[/tex]
  • [tex]q_{new}= 30 \% \,of \,new\, quantity = 0.3(7+x)[/tex]

Now the equation is as

                                  [tex]q_{old}+q_{added}=q_{new}\\0.7+x=0.3(7+x)\\0.7+x=2.1+0.3x\\x-0.3x=2.1-0.7\\0.7x=1.4\\x=2 \, litres[/tex]

So 2 litres of pure alcohol will be added to make the overall concentration of 9 litres of mixture as 30%.

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