Question

A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solutioncontains 80% pure antifreeze. The company wants to obtain 320 gallons of a mixture that contains 40% pure antifreeze. How many gallons of water and howmany gallons of the premium antifreeze solution must be mixed?Water: gallonsPremium antifreeze: gallons

Answer 1

ANSWER:

Water: 80 gallons

Premium antifreeze: 240 gallons

STEP-BY-STEP EXPLANATION:

Given:

Let x amount of water required

An equation based on the the percent water, an 80% solution is 20% water.

Therefore, we can establish the following equation:

$\begin{gathered} 0.2\cdot(320-x)+x=0.4\cdot320 \\ \text{ solving for x:} \\ 64-0.2x+x=128 \\ 0.8x=128-64 \\ x=\frac{64}{0.8} \\ x=80\text{ gallons} \end{gathered}$

So that's 80 gallons of water and that's 240 (320-80) gallons of premium antifreeze.