How many liters of each solution should be used?

Question

A chemist has three different acid solutions. The first acid solution contains 20% acid, the second contains 40% and the third contains 85%. They want to use all three solutions to obtain a mixture of 60 liters containing 65% acid, using 2 times as much of the 85% solution as the 40% solution. How many liters of each solution should be used?

The chemist should use _____ liters of 20% solution, _____ liters of 40% solution, and _____ liters of 85% solution.

Answer 1

.20x+.40y + .85z = .65(60)

z =2y

x+y+z = 60

.2x +.2y +.2z = .2(60)

.2y + .65z = .45(60)

.2y +.65(2y) = 27

1.5y = 27

y = 27/1.5 = 18 Liters of 40%

z=2y = 36 Liters of 85%

x = 60-18-36 = 6 Liters of 20%

.2(6)+.4(18)+.85(36)

= 1.2 + 7.2 + 30.6

= 39=.65(60)

6+18+36 = 60 Liters total

here's a slightly different problem, using 25% instead of 20%

it shows the same basic method

25x +.4y + .85z = .65(60)

z=2y

x+y+z = 60

use substitution, elimination or matrix algebra

.25x +.25y +.25z = .25(60)

subtract last equation from 1st

.15y + .6z = .4(60)

.15y +.6(2y) = 24

1.35y =24

y = 24/1.35 = 17 7/9 Liters of 40%

z = 35 5/9 Liters of 85%

x =60-17 7/9 -35 5/9 = 60-53 1/3= 6 2/3 Liters of 25%

6 2/3 + 35 5/9 + 17 7/9 = 60 Liters of 65%