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 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

120 gal. 0% water mixed with 60 gal premium 60%

gives 180 gallons of 20%

.6x + 0 = .2(180) = 36

x =36/.6 = 120