Achemical company makes two brands of antifreeze. the first brand is 65% pure antifreeze, and the second brand is 95% pure antifreeze. in order to obtain 90 gallons of a mixture that contains 90% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Let us represent the gallons of 65% antifreeze as x. If the total volume is 90 gallons, then the amount of 95% antifreeze can be written as (90 - x). Then we add up the total amount of antifreeze based on the volumes and percentages:
(0.65)x + (0.95)(90 - x) = (0.90)(90)
0.65x + 85.5 - 0.95x = 81
-0.3x = -4.5
x = 15
90 - x = 75
Therefore, 15 gallons of 65% antifreeze and 75 gallons of 95% antifreeze were used.