Question

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.

Answer 1

A and B

Explanation:

i took the test

Answer 2

Let

x-------> the amount of
`2\%` solution

y--------> the amount of
`7\%` solution

we know that

`2\%=0.02\\7\%=0.07\\3.5\%=0.035`

so

`x+y=1`

`y=1-x` -------> equation A

`0.02x+0.07y=0.035` -------> equation B

substitute equation A in equation B

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

`0.02x+0.07-0.07x=0.035`

`0.05x=0.035`

`x=0.7\ liters`

find the value of y

`y=1-x`

`y=1-0.7=0.3\ liters`

therefore

The student need
`0.7\ liters` of
`2\%` solution and
`0.3\ liters` of
`7\%` solution

the answer is

A) The percent values were written incorrectly in the equation

B) The amount of 7% solution should be written as 1 – x, not x – 1.