A scientist needs 10 liters of a 20% acid solution for an experiment, but she only has 5 percent solution and a 40% solution. To the nearest tenth of a liter, about how many liters of 5% and the 40% solutions should she mix to get the solution she needs
Let x represent the number of liters of the 5% solution needed.
Therefore, 10 - x represents the number of liters of the 40% solution needed.
To solve the problem, we can set up the following equation:
0.05x + 0.40(10 - x) = 0.20(10)
The equation represents the sum of the acid content in the 5% solution (0.05x) and the 40% solution (0.40(10 - x)) being equal to the acid content in the desired 20% solution (0.20(10)).
Simplifying the equation, we have:
0.05x + 4 - 0.40x = 2
Combining like terms, we get:
-0.35x + 4 = 2
Subtracting 4 from both sides, we have:
-0.35x = -2
Dividing both sides by -0.35, we get:
x ≈ 5.7
Therefore, she should mix approximately 5.7 liters of the 5% solution and 10 - 5.7 = 4.3 liters of the 40% solution to obtain 10 liters of the desired 20% acid solution.