Achemical company makes two brands of antifreeze. the first brand is 65% pure antifreeze, and the second brand is 90% pure antifreeze. in order to obtain 160 gallons of a mixture that contains 70% pure antifreeze, how many gallons of each brand of antifreeze must be used?

When two material with different concentrations of the same active ingredient are mixed, the active ingredient before and after mixing remains constant. If the volume of the first brand is assigned x gallons, the volume of the second brand is (160-x) gallons.  Therefore, according to the above principle, (65%)(x) + (90%)(160-x) = (70%)(160), 0.65x+ 144-0.9x = 112, x=128 gallon. 128 gallon of the first brand (65%) and 160-128 = 32 gallon of the second brand (90%) of antifreeze must be used.