Mixture Word Problem

Question

A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 90% pure antifreeze. In order to obtain 90 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

.9x + (90-x).65 = 90(.75

(.9-.65)x = 90(.75) -90(.65) = .1(90) = 9

.25x = 9

x = 36 gallons of 90% mixed with 54 gallons of 65% yield 90 gallons of 75%

65 is within 10 of 75

90 is within 15 of 75

15/10=3/2 = 54/36

you need 1.5 times as much 65% as 90%