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A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 45% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer :

The gallons of the first brand of antifreeze should be 60 gallons.

The gallons of the second brand of antifreeze should be 90 gallons.

What are the linear equations that represent the question?

0.2f + 0.45s = 52.50 (0.35 x 150) equation 1

f + s = 150  equation 2

Where:

  • f = gallons of the first antifreeze
  • s =  gallons of the second antifreeze

how many gallons of each brand of antifreeze must be used?

Multiply equation 2 by 0.2

0.2f + 0.2s = 30 equation 3

Subtract equation 3 from equation 2

0.25s = 22.50

s = 22.50 / 0.25

s = 90

f = 150 - 90 = 60 gallons

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