Question

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?

Answer 1

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

Step-by-step explanation:

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

• 
  `n_(old)=7` litres
• 
  `n_(new)=7+x` litres

Also the quantity of alcohol is given as

• 
  `q_(old)=10 \% \, of \, 7 \, litres =0.7`

• 
  `q_(added)=x`

• 
  `q_(new)= 30 \% \,of \,new\, quantity = 0.3(7+x)`

Now the equation is as

`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`

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