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.

Question

Monique Hodges

Mathematics

8 May, 10:18

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.

+2

Answers (1)

Know the Answer?

Mario Johns · Answer 1

The equation was incorrect, it should have been:

(0.02x+0.07 (1-x)) = 0.035

.02x+.07-.07x=.035

-.05x=-.035

x=.7

So he will need 700ml of 2% mixed with 300ml of 7% to make 1000ml of 3.5%