Question

A chemical company makes two brands of antifreeze. The first brand is 55% pure antifreeze, and the second brand is 80% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

102 gallons of 55% antifreeze

68 gallons of 80% antifreeze

Explanation:

55% antifreeze: x

80% antifreeze: y

x + y = 170 ===> -.55(x + y = 170) ===> -.55x - .55y = -93.5

.55x + .80y = .65(170) ===> .55x + .80y = 110.5

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add the two equations to eliminate a variable: 0.25y = 17

divide by 0.25 to isolate y: y = 68

substitution to find x:

x + y = 170

x + 68 = 170

x = 102