Question

A chemist wants to mix a solution of 75% concentrate with 6 liters of 20% concentrate. How many liters of the 75% concentrate must be used to produce a concentrate of 45%?

Answer 1

Let's start by creating the equation that will describe the concentration of the mixture by the number of liters of each solution we use. The concentration of a solution is given by sum of the concentrations of each solution times the amount used, divided by the total quantity, or:
\[c = \frac{ 0.75x + 0.2y }{ x + y }\] where c is the final concentration, x is the number of liters of 75% concentration solution, and y is the number of liters of 20% concentration solution.
We know that we are using 6 liters of 20% concentration solution (y), and that our goal is a solution of 45% (c), so let's plug those in:
\[0.45 = \frac{ 0.75x + 0.2*6 }{ x + 6 }\] Now we simply solve for x.
\[0.45 = \frac{ 0.75x + 1.2 }{ x + 6 }\]\[0.45(x + 6) = 0.75x + 1.2\]\[0.45x + 2.7 = 0.75x + 1.2\]\[0.3x = 1.5\]\[x = 5\]So we need 5 liters of the 75% solution to make a solution of 45% concentration.

Answer 2

\(\huge\color{red}{\bigstar}\color{orange}{\bigstar}\color{yellow}{\bigstar}\color{lightgreen}{\bigstar}\color{green}{\bigstar}\color{turquoise}{\bigstar}\color{royalblue}{\bigstar}\color{purple}{\bigstar}~\color{#00bfff}{\bigstar}\color{#00bfff}{\bigstar}\color{#00bfff}{\bigstar}\color{#11c520}{\bigstar}\color{#11c520}{\bigstar}\color{#11c520}{\bigstar}\\\huge\cal\color{red}W\color{orange}E\color{goldenrod}L\color{yellow}C\color{lightgreen}O\color{darkgreen}M\color{turquoise}E~~\color{royalblue}T\color{purple}O~~\color{#00bfff}{Open}\color{#11c520}{Study}\\\huge\color{red}{\bigstar}\color{orange}{\bigstar}\color{yellow}{\bigstar}\color{lightgreen}{\bigstar}\color{green}{\bigstar}\color{turquoise}{\bigstar}\color{royalblue}{\bigstar}\color{purple}{\bigstar}~\color{#00bfff}{\bigstar}\color{#00bfff}{\bigstar}\color{#00bfff}{\bigstar}\color{#11c520}{\bigstar}\color{#11c520}{\bigstar}\color{#11c520}{\bigstar}\)