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

Question

Please solve the math with formulas

Answer 1

Let x be the amount in litres of the 100% alcohol (pure alcohol).

10% of 7 litres is 0.7L alcohol. There are x litres of pure alcohol.

The total quantity of the mixture is 7+x litres.

The amount of alcohol is 0.7+x=0.3(7+x) because the mixture contains 30% alcohol.

So 0.7+x=2.1+0.3x, 0.7x=2.1-0.7=1.4, x=1.4/0.7=14/7=2L.

2 litres of pure alcohol are needed to make a 30% alcohol mixture.