Question

A scientist needs 10 litera of a 20% acid solution for an experiment but she has only 5% solution and a 40% solution. To the nearest tenth of a liter, how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?

Answer 1

x = liters of 5% solution

y = liters of 40% solution

The scientist wants 10 L total of a 20% solution, so

x + y = 10

0.05 x + 0.40 y = 0.20 (x + y) = 2

From the first equation,

y = 10 - x

Substitute this into the second equation and solve for x :

0.05 x + 0.40 (10 - x) = 2

0.05 x + 4 - 0.40 x = 2

2 = 0.35 x

x ≈ 5.714 L

Solve for y :

y = 10 - x

y ≈ 4.286 L