A pharmacist wishes to strennghten a mixture that is 10% alchohol to one that is 30% alchohol. How much pure alchohol should be added to 7 liters of the 10% mixture?
7 litres of 10% mixture contain 0.7 litres of alcohol.
Add x litres of pure alcohol to the current 7 litres of 10% mixture.
Volume of new mixture is (7 + x) litres.
Amount of alcohol in this new mixture is (0.7 + x) litres.
Concentration of new mixture is (0.7 + x) / (7 + x) = 30% = 0.3
0.7 + x = 0.3(7 + x) = 2.1 + 0.3x
x - 0.3x = 2.1 - 0.7
0.7x = 1.4
x = 2
Answer: add 2 litres of pure alcohol to the original mixture