RIght answer gets a mark. Plus 20 pts. A chemical company makes two brands of antifreeze. The first brand is 60 % pure antifreeze, and the second brand is 75 % pure antifreeze. In order to obtain 180 gallons of a mixture that contains 70 % pure antifreeze, how many gallons of each brand of antifreeze must be used?

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Mathematics

5 July, 01:58

RIght answer gets a mark. Plus 20 pts. A chemical company makes two brands of antifreeze. The first brand is 60 % pure antifreeze, and the second brand is 75 % pure antifreeze. In order to obtain 180 gallons of a mixture that contains 70 % pure antifreeze, how many gallons of each brand of antifreeze must be used?

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Davion · Answer 1

x = gallons of 60% antifreeze

y = gallons of 75% antifreeze

x + y = 180

Each gallon of the 60% brand contributes 0.6x gallons of antifreeze, and each gallon of the 75% brand contributes 0.75 gallons. The company wants the new brand to have a concentration of 70% antifreeze, so that each gallon of it contains 0.7*180 = 126 gallons of antifreeze.

0.6x + 0.75y = 126

Solve for x and y:

x + y = 180 = => y = 180 - x

0.6x + 0.75y = 126 = => 0.6x + 0.75 (180 - x) = 126

==> 0.6x + 135 - 0.75x = 126

==> 9 = 0.15x

==> x = 60 = => y = 120