How many gallons of each brand of antifreeze must be used?

Question

A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 80% pure antifreeze. In order to obtain 120 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

.8x + .4(120-x) = .75(120)

.8x -.4x = .75(120)- .4(120)

.4x = .35(120)

x = .35(120)/.4 = .35(30)/.1 = 3.5(30) = 35(3) = 105 gallons of 80% and 15 gallons of 40%

yield a mixture of 120 gallons of 75%

80-75 = 5

75-40 = 35

you need 7 times as much 80% as 40%

7x+x = 8x = 120

x = 120/8 = 15 gallons of 40%

105 gallons of 80%