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

Question

2 months ago

7

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? Explain

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-03-23T21:30:32+03:00

<span>5.7 liters of a 5% solution combined with 4.3 liters of a 40% solution. To begin, define the problem with formulas. x Represents the liters of the 5% solution utilized. 10-x Represents the liters of the 40% solution used. This forms an equation: 5% of x plus 40% of (10-x) equals 20% of 10. 0.05x + 0.40(10-x) = 0.20 * 10 Now, distribute the 0.40 coefficient. 0.05x + 4.0 - 0.40x = 0.20 * 10 Next, combine the terms. 4.0 - 0.35x = 2.0 Add 0.35x to each side. 4.0 = 2.0 + 0.35x Subtract 2 from both sides. 2.0 = 0.35x Lastly, divide both sides by 0.35. 5.7 = x Thus, 5.7 liters of a 5% solution is required. To determine the volume of the 40% solution, subtract from 10. 10.0 - 5.7 = 4.3</span>