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. About how many liters of the 5% and the 40% solutions should the scientist mix to get the solution she needs?

Choose the equation to match the situation.
A. (0.20)(10) = 0.05x + 0.40x
B. (0.20)(10) = 0.05x + 0.40(10 − x)
C. (0.20)(10) = 0.05(10) + 0.40(10 − x)
D. (0.20)(10) = 0.05(10 − x) + 0.40(10 − x)
Part B

Round the answers to the nearest tenth.

She should mix
liters of 5% solution with
liters of 40% solution.

Answer 1

Answer: B.

Let x = liters of 5% solution, so 10 − x = liters of 40% solution.
Equation: 0.20(10) = 0.05x + 0.40(10 − x).

Solve:
2 = 0.05x + 4 − 0.40x = 4 − 0.35x
0.35x = 2 → x = 2 / 0.35 = 40/7 ≈ 5.7 L

40% amount = 10 − x = 30/7 ≈ 4.3 L

She should mix about 5.7 L of 5% solution with 4.3 L of 40% solution.