Question

during a college chemistry experiment, students must prepare 33 fluid ounces of a solution that contains 5% ethylene glycol. to make this, the students will mix one solution containing 2% ethylene glycol with another that contains 12% ethylene glycol. how much of each should the students use?
write your answers as whole numbers or as decimals rounded to the nearest tenth.
fluid ounces of 2% solution
fluid ounces of 12% solution

Explanation:

Step1: Set up equations

Let \(x\) be the amount of \(2\%\) solution and \(y\) be the amount of \(12\%\) solution.
We have two equations:
\(x + y=33\) (total volume)
\(0.02x + 0.12y=0.05\times33\) (ethylene glycol amount)
From \(x + y = 33\), we get \(x=33 - y\)

Step2: Substitute and solve

Substitute \(x = 33 - y\) into \(0.02x+0.12y = 0.05\times33\)
\(0.02(33 - y)+0.12y=1.65\)
\(0.66-0.02y + 0.12y=1.65\)
\(0.1y=1.65 - 0.66\)
\(0.1y=0.99\)
\(y = 9.9\)

Step3: Find \(x\)

Substitute \(y = 9.9\) into \(x=33 - y\)
\(x=33-9.9 = 23.1\)

Answer:

23.1 fluid ounces of \(2\%\) solution
9.9 fluid ounces of \(12\%\) solution