System of equations word problems

Question

A chemists needs 30 liters of a 10% alcohol solution but has only a 30% alcohol solution. How many liters of 30% solution and water should he mix to make the desired 30 liters of 10% solution?

Answer 1

Consider that the amount of alcohol will be the liters of solution times the percentage of alcohol. So 30 liters of 10% alcohol would have 30 x 0.10 of pure alcohol (or 3 liters). Also consider that water is a 0% solution of alcohol.

Let x be the amount (liters) of 30% solution and let y be the amount (liters) of water. Then x + y = 30 (because the amount of water and 30% solution needs to add together to get 30 liters). Also 0.30x + 0y = 0.10(30) because x liters of 30% solution mixed with y liters of 0% solution must equal the amount of pure alcohol in 30 liters of 10% solution.

Taking the last equation and solving for x we get:

0.30x + 0y = 0.10(30)

0.30x + 0 = 3

0.30x = 3

x = 10

since x + y = 30 then y = 20

So, 10 liters of 30% solution mixed with 20 liters of water gives 30 liters of 10% solution

Answer 2

Hope this helps!