A chemical company makes two brands of antifreeze. The first brand is 35% anti freeze, and the second brand is 85% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used.

Answer: There are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.Step-by-step explanation:Since we have given that Percentage of anti freeze in first brand = 35%Percentage of anti freeze in second brand = 85%Percentage of anti freeze in mixture = 75%Total number of gallons of mixture = 150 gallonsWe will use " Mixture and Allegation":  First brand         Second brand       35%                      85%                       75%------------------------------------------------------------------85%-75%         :            75%-35%     10                :               40      1                 :                 4So, Number of gallons of anti freeze in first brand is given by[tex]\dfrac{1}{5}\times 150\\\\=30\ gallons[/tex]Number of gallons of anti freeze in second brand is given by[tex]\dfrac{4}{5}\times 150\\\\=40\times 3\\\\=120\ gallons[/tex]Hence, there are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.