Brine is a solution of salt and water. If a tub contains 70 pounds of a 5% solution of brine, how much water (to the nearest tenth lb.) must evaporate to change it to an 7.5% solution?

Question

Mathematics

Stephanie Hughes

4 July, 05:59

Brine is a solution of salt and water. If a tub contains 70 pounds of a 5% solution of brine, how much water (to the nearest tenth lb.) must evaporate to change it to an 7.5% solution?

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Answers (1)

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Ramon Bryan · Answer 1

We first model the equation that expresses the problem. We let x be the amount of water evaporated.

0.05 (70) = (0.075) (70-x)

Take note that we modeled this expression by keeping in mind that the amount of solute (salt) will always be equal, and it is the solvent (water) that will change therefore affecting the percentage of the concentration of the solution.

Solving for x:

70 - x = 0.05 (70) / (0.075)

x = 23.3 lbs of water.