To prepare 10 liters of a 2% acid solution by mixing only a 1% acid solution and a 4% acid solution, we can use the method of solving a system of equations based on the total volume and acid concentration. Let:

• xxx = liters of 1% acid solution
• yyy = liters of 4% acid solution

We know:

• Total volume: x+y=10x+y=10x+y=10
• Total acid content: 0.01x+0.04y=0.02×10=0.20.01x+0.04y=0.02\times 10=0.20.01x+0.04y=0.02×10=0.2 liters of pure acid

From the first equation, y=10−xy=10-xy=10−x. Substitute into the second:

0.01x+0.04(10−x)=0.20.01x+0.04(10-x)=0.20.01x+0.04(10−x)=0.2

0.01x+0.4−0.04x=0.20.01x+0.4-0.04x=0.20.01x+0.4−0.04x=0.2

−0.03x=0.2−0.4=−0.2-0.03x=0.2-0.4=-0.2−0.03x=0.2−0.4=−0.2

x=−0.2−0.03=0.20.03≈6.7 litersx=\frac{-0.2}{-0.03}=\frac{0.2}{0.03}\approx 6.7\text{ liters}x=−0.03−0.2​=0.030.2​≈6.7 liters

Then,

y=10−6.7=3.3 litersy=10-6.7=3.3\text{ liters}y=10−6.7=3.3 liters

So, the scientist should mix approximately 6.7 liters of the 1% acid solution and 3.3 liters of the 4% acid solution to get 10 liters of a 2% acid solution, rounded to the nearest tenth of a liter

. This approach follows the principle of conservation of acid amount when mixing solutions of different concentrations