Question

A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 140 gallons of a mixture that contains 65% pure antifreeze. How many gallons of each brand of antifreeze must be used?

Answer 1

If a chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 95% pure antifreeze. The number of  gallons each brand of antifreeze must be used is: 56 gallons of 20% antifreeze and 84 gallons of 95% antifreeze.

Number of  gallons for each brand of antifreeze

Let call x = The amount of 20% pure antifreeze needed

Let  140 - x = amount of 95% antifreeze needed

Hence,

x gallons of 20% antifreeze + (140-x) gallons of 95% = 140 gallons of 65%

Thus,

.20x + .95(140-x) = .65(140)

.20x + 133 - .95x = 91

Collect like terms

42= .75x

Divide both side by .75x

x=42/.75

x=56

Hence,

56 gallons of 20% antifreeze

84 gallons of 95% antifreeze

Therefore the number of  gallons each brand of antifreeze must be used is: 56 gallons of 20% antifreeze and 84 gallons of 95% antifreeze.

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