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? Explain

Answer 1

5.7 liters of 5% solution and 4.3 liters of 40% solution. First, create some formulas to define the problem. x Amount of 5% solution used 10-x Amount of 40% solution used This equation means 5% of x plus 40% of (10-x) equals 20% of 10. 0.05x + 0.40(10-x) = 0.20 * 10 Distribute the 0.40 0.05x + 4.0 - 0.40x = 0.20 * 10 Combine terms 4.0 - 0.35x = 2.0 Add 0.35x to both sides 4.0 = 2.0 + 0.35x Subtract 2 from both sides 2.0 = 0.35x Divide both sides by 0.35 5.7 = x So we need to use 5.7 liters of the 5% solution. To get the amount of 40% solution, just simply subtract from 10. 10.0 - 5.7 = 4.3