mixture percent question

Question

A chemical company makes two brands of antifreeze. The first brand is 55% pure antifreeze, and the second brand is 85% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

.85x + .55(180-x) = .75(180)

.3x = 135 - .55(180) = 135-99 = 36

x = 36/.3 = 12/.1 = 120

x = 120 gallons of 85% and

180-120 = 60 gallons of 55%

to get

180 gallons of 75%

55 is within 20 of 75

85 is within 10 of 75

you need 20/10 =2 = twice as much 85 as 55

120 is twice 60