Linear equation

Question

A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze and the second brand is 60% pure antifreeze. I’m order to obtain 110 gallons of a mixture that contains 40% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

60-40=20

40-35 =5

20/5 =4.

4 times as much 35% as 60% is needed

(110-x)/x = 4

4x = 110-x

5x =110

x =110/5=22 gallons of 60%,

110-22 = 88 gallons of 35%

.

.6(22) +.35(88) = 13.2 + 30.8=44

.4(110)=44

but here's how they usually set up the problem and solve it:

.6x + .35y = .4(110)

.6x + .35(110-x) = .4(110)

.6x -.35x = .4(110)-.35(110)

.25x = .05(110)

x = 5.5/.25 = 22 gallons of 60%

y = 110-22 = 88 gallons of 35%