How many liters of each solution should be used?

Question

A chemist has three different acid solutions. The first acid solution contains 20%20% acid, the second contains 30%30%and the third contains 75%75%. They want to use all three solutions to obtain a mixture of 120120 liters containing 35%35%acid, using 22 times as much of the 75%75% solution as the 30%30% solution. How many liters of each solution should be used?

Answer 1

.2F + .3S + .75T = .35(120)

T=22S

.2F + .3S +.75(22S) = 42

.2F + .3S + 16.5S = 42

.2F + 16.8S = 42

S=(120-F)/23

.2F + 16.8(120-F)/23 = 42

4.6F -16.8F +16.8(120) =42(23)

4.6F -16.8F = 42(23) -16.8(120)

12.2F = -966+2016= 1050

F =1050/12.2= 86.07 liters for First solution

S=1.48 liters for Second solution

T=32.46 liters for Third solution

.2(86.1) + .3(1.5) + .75(32.5 = 17.2 + .45 + 24.4= 42