Question

A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze and the second brand is 55% pure antifreeze. In order to obtain 160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Answer:

• 64 gallons 30%
• 96 gallons 55%

Step-by-step explanation:

The amount of each brand can be found by writing and solving an equation that makes use of the given relations.

Setup

Let x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...

  0.55x +0.30(160 -x) = 0.45(160)

Solution

Subtracting 0.30(160), we have ...

  x(0.55 -0.30) = 160(0.45 -0.30)

  x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x

96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.

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