How many liters of each solution should be used?

Question

A chemist has three different acid solutions. The first acid solution contains  acid, the second contains  and the third contains . He wants to use all three solutions to obtain a mixture of  liters containing  acid, using  times as much of the  solution as the  solution. How many liters of each solution should be used?

The chemist should use(______) liters of solution

 (______) liters of solution

 (_____) liters of  solution

Answer 1

Let F = first solution of 15%

S = 2nd solution of 35%

T = 3rd of 55%

F+S+T = 70

T=3S

15F+35S + 55T = 45(70)= 3150

3 equations, 3 unknowns, there should be a unique solution

F=70-S-T = 70-S -3S = 70-4S

15(70-4S) + 35S + 55(3S) = 3150

1050 - 60S + 35S + 165S = 3150

140S = 3150-1050 = 2100

S = 2100/140 = 210/14 = 30/2 = 15

T=3S = 45

F = 70-4S =70-60=10

10 of 15%

15 of 35%

45 of 55%

to get 70 of 45%