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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 liter 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.
What errors did the student make? Check all that apply.
The percent values were written incorrectly in the equation.
The amount of 7% solution should be written as 1 – x, not x – 1.
The equation as written is solved incorrectly. x ≠ 1.17.
x must represent the amount of the more highly concentrated solution.
The interpretation is incorrect. 1 liter of 2% solution is needed to make 1.17 liters of 3.5% solution.
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