Solving a percent mixture problem using a system of linear equations

Question

A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60% pure antifreeze. The company wants to obtain 180 gallons of a mixture that contains 20% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?

Water: gallons

Premium antifreeze: gallons

Answer 1

Let x = amount of water to be added

60% solution of antifreeze is 40% water

20% solution of antifreeze is 80% water

So, 1.00x + 0.40(180 - x) = 0.80(180)

Solve for x.