A chemist needs to create a 25% acid solution by mixing a 10% acid solution and a 40% acid solution. How much of each solution is required to make 100 liters of the 25% solution?
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Let x be the amount of the 10% acid solution needed.
Then, the amount of the 40% acid solution needed is 100 - x.
The amount of acid in the 10% acid solution is 10/100 * x = x/10.
The amount of acid in the 40% acid solution is 40/100 * (100 - x) = 40 - 4x/10.
The total amount of acid in the 25% acid solution is 25/100 * 100 = 25.
So, x/10 + (40 - 4x)/10 = 25.
This simplifies to 2x + 40 - 4x = 250.
Combining like terms, we get 2x - 4x = 250 - 40.
This simplifies to -2x = -210.
Dividing both sides by -2, we get x = 105.
Thus, 105 liters of the 10% acid solution are needed, and 100 - 105 = -5 liters of the 40% acid solution are needed.
Since the amount of the 40% acid solution is negative, the chemist cannot make a 25% acid solution by mixing a 10% acid solution and a 40% acid solution.
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