Question

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

Answer 1

5.7 liters of 5% solution and 4.3 liters of 40% solution is needed to be mixed to get 10 liters of a 20% acid solution

Explanation:

Let

x = Amount of 5% solution needed

(10 - x) = Amount of 40% solution needed

Equation:

5% of x + 40% of (10-x) = 20% of 10

0.05x + 0.40(10-x) = 0.20 * 10

Open parenthesis

0.05x + 4.0 - 0.40x = 0.20 * 10

Collect like terms

4.0 - 0.35x = 2.0

Add 0.35x to both sides of the equation

4.0 = 2.0 + 0.35x

Subtract 2.0 from both sides of the equation

2.0 = 0.35x

Divide both sides by 0.35

2.0 / 0.35 =x

5.7 = x

5.7 liter of the 5% solution is needed

Next is to find the amount of 40% solution needed

(10 - x) = Amount of 40% solution used

Amount of 40% solution used = 10 - 5.7

= 4.3

4.3 liters of 40% solution is needed