Brine is a solution of salt and water. If a tub contains 50 pounds of 5% solution of brine, how much water (to the nearest tenth lb.) must evaporate to change it to an 8% solution?

Question

Riley Roberts

Mathematics

14 October, 13:37

Brine is a solution of salt and water. If a tub contains 50 pounds of 5% solution of brine, how much water (to the nearest tenth lb.) must evaporate to change it to an 8% solution?

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Karina Morton · Answer 1

The only important thing here is the ratio between the salt and the entire solution. The salt makes up 5% of the entire solution, which is 50lbs. 5% of 50lbs is 2.5lbs. So, we want to know how much brine must be left to create a 8% solution with 2.5lbs of salt. To do this, make the amount of brine solution a variable, x. So, you know that 2.5 should be 8% of x. This can be modeled by the equation 2.5/x = 0.08. Solve for x. Now that you've got the amount of brine, 31.25lbs, you've got to subtract that from the original to see how much water has evaporated. 50 - 31.25 = 18.75. Round up to 18.8lbs and there's your answer!