how many liters of water must be added to 30 liters of a 28% salt solution to dilute it to a 12% solution?

Question

HELP! THIS HW IS SO HARD :(

Answer 1

This is a mixture problem.

Let
x = amount of water added
x + 30 = amount of solution after water is added

The water has 0% salt in it. Notice, the amount of salt does not change. Only its concentration changes.

30*.28 + x*0 = (x + 30)*.12
8.4 + 0 = .12x + 3.6
4.8 = .12x
.12x = 4.8
x = 4.8/.12 = 40 liters

You need to add 40 liters of water.

Answer 2

required volume of water be v liters, then
30L of 28% + vL water = (30 + v)L of 12%
=> 30*28/100 = (30 + v)*12/100
=> v = 70 -- 30 = 40
40 liters of water is required to be added.