How many liters of each solution should be used?

Question

A chemist has three different acid solutions. The first acid solution contains 15% acid, the second contains 35% and the third contains 55%. He wants to use all three solutions to obtain a mixture of 266 liters containing 25% acid, using 3 times as much of the 55% solution as the 35% solution. How many liters of each solution should be used?

Answer 1

Good evening Sam,

Let F, S, and T be the first, second, and third solutions respectively in Liters.

When we combine the three solutions, we get

F + S + T = 266.

But we are to use three times the third amount as the second amount

→ T = 3S

→ F + S + 3S = 266

→ F + 4S = 266

→ F = 266 - 4S {Eq 1}

Now, just looking at the amount of acid in each solution, and wanting the result to be 25% acid, we have

.15F + .35S + .55T = .25(266). By substituting out T for 3S, and simplifying the right side

→ .15F + .35S + .55(3S) = 66.5

→ .15F + .35S + 1.65S = 66.5

→ .15F + 2S = 66.5 {Eq 2}

Using {Eq 1} and {Eq 2}, we get

.15(266 - 4S) + 2S = 66.5

→ 39.9 - .6S + 2S = 66.5

→ 1.4S = 26.6

→ S = 19

→ F = 266 - 4(19) = 266 - 76 = 190

→ T = 3(19) = 57

Thank you for the question.

Michael E