To obtain 126 L of a 60% acid solution, the chemist needs to mix 36 L of a 10% acid solution and 90 L of an 80% acid solution.
To determine how many liters of a 10% acid solution and an 80% acid solution must be mixed together to obtain 126 L of a 60% acid solution, you can use the following steps:
1. Let x represent the liters of the 10% acid solution and y represent the liters of the 80% acid solution.
2. You know that the total volume of the mixture is 126 L, so you can write the equation: x + y = 126.
3. You also know that the mixture needs to be a 60% acid solution, so you can write the equation: 0.1x + 0.8y = 0.6 * 126, which simplifies to 0.1x + 0.8y = 75.6.
4. Now you have a system of linear equations:
x + y = 126
0.1x + 0.8y = 75.6
5. Solve for one variable, for example, x = 126 - y.
6. Substitute the expression for x in the second equation: 0.1(126 - y) + 0.8y = 75.6.
7. Simplify the equation: 12.6 - 0.1y + 0.8y = 75.6.
8. Combine the y terms: 0.7y = 63.
9. Solve for y: y = 63 / 0.7 = 90.
10. Substitute the value of y back into the equation for x: x = 126 - 90 = 36.
So, to obtain 126 L of a 60% acid solution, the chemist needs to mix 36 L of a 10% acid solution and 90 L of an 80% acid solution.