Question

A chemist has 200 mL of a 10% sucrose solution. She adds x mL of a 40% sucrose solution. The percent concentration, y, of the final mixture is given by the rational function:
y=0.1(200)+0.4x/200+x * 100

The chemist needs the concentration of the final mixture to be 30%. How many milliliters of the 40% solution should she add to the 10% solution to get this concentration?
mL

Answer 1

Answer:

The chemist needs to add 400mL of 40% solution.

Step-by-step explanation:

The equation

$y=\frac{0.1(200)+0.4x}{200+x} *100$

gives the percent concentration $y$ of the final mixture, when $x$ mL of the 40% solution are added.

Now we are asked, how many milliliters $x$ of the 40% solution should the chemist add to get final percent concentration $y=30$; this is just a matter of solving the equation

$30=\frac{0.1(200)+0.4x}{200+x} *100$

and we solve it the following way:

$30=\frac{0.1(200)+0.4x}{200+x} *100\\\\0.3 =\frac{0.1(200)+0.4x}{200+x}\\\\0.3(200+x)=0.1(200)+0.4x\\\\60+0.3x=20+0.4x\\\\40=0.1x\\\\x=\frac{40}{0.1} \\\\\boxed{x=400\:mL}$

Thus, the chemist needs 400mL of 40% solution to get 30% concentration of the final mixture.