A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 lit
er of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation: 0.2x + 0.7(x – 1) = 0.35(1)
He solves the equation and determines that x is about 1.17 liters. He interprets this as needing 1.17 liters of 2% solution to make 1 liter of 3.5% solution
The student clearly made a mistake, because he found that he needs to mix more solution that he wants to end up with. Mixing 1.17 L of one solution with more of some other solution will make more than 1 L of another solution.
The mistake is writing <em>x</em> - 1 instead of 1 - <em>x</em>.