Question

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

Equation:________________________

Solution:____ liters of 5% and _____ liters of 40%

Answer 1

Equation: X × 0.4 + (10 - X)×0.05 = 10 × 0.2

Solution: 5.71 liters of 5% and 4.29 liters 40%

Explanation:

The volume of the 20% acid solution the scientist needs = 10 liters

The concentration of the solution she has = 5% and 40%

Therefore, we have;

X volume of the 40% solution is mixed with 10 - X volume of the 5% solution, to obtain 10 liters of the 20% solution

Therefore, we have;

Equation: X × 0.4 + (10 - X)×0.05 = 10 × 0.2

0.4·X + 0.5 - 0.05·X = 2

0.35·X = 2 - 0.5 = 1.5

X = 1.5/0.35 = 30/7

∴ The volume of the 40% solution = 30/7 liters ≈ 4.29 liters

The volume of the 5% solution = 10 - X = 10 - 30/7 = 40/7 liters ≈ 5.71 liters

Therefore, we have;

5.71 liters of 5% solution and 4.29 liters 40% solution.