Question

Brine is a solution of salt and water. If a tub contains 50 gallons of a 5% solution of brine, how much water must

Answer 1

Let $w$ be the amount of water that evaporates. At the start, the solution in the tub consists of 2.5 gallons of salt (5% of 50 gallons). After $w$ gallons of water evaporates, we're left with a solution with total volume $50-w$ gallons, and 8% of this amount should be salt, or $0.08(50-w)$ gallons of salt. The amount of salt in the tank before and after evaporation remains unchanged, so

$2.5=0.08(50-w)\implies2.5=4-0.08w\implies0.08w=1.5\implies\boxed{w=18.75}$

gallons of water need to be evaporated.