Pedro is in a chemistry lab making solutions. Pedro added a 75% acid solution to 10 milliliters of solution that is 15% acid.

The function that represented the percent of acid in the resulting solution was:

f(x) = numerator 10(0.15) + x(0.75) denominator 10 + x 10(0.15) + x(0.75) 10 + x

where x is the amount of 75% solution added.

Let's consider how certain factors affect the situation. Answer the following questions using your notes.

1. Can the resulting solution ever be 10% acid? If so, how much of the 75% solution should be added? If not, why not?
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No, you cannot have a solution with less than 15% acid. Consider if Pedro adds nothing, the amount of acid is 15%. However, he is adding more solution and the solution he is adding has a lot more acid in it than 15%. That means that the overall percentage of acid in the resulting solution will be greater than 15%.

2. Can the resulting solution ever be 85% acid? If so, how much of the 75% solution should be added? If not, why not?
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No, you cannot have a solution with more than 75% acid. Consider that the greatest amount of acid Pedro has is 75%. Even if Pedro didn’t start out with the 15% solution, which is much lower than 75%, the greatest percent of acid he could have is 75%.

3. What is a reasonable domain for the situation?
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A reasonable domain would be 0 ml to maximum amount of ml of 75% solution that Pedro has available. 0 < x ≤ all of the 75% acid solution that Pedro has. The domain is the set of numbers that represents the independent variable, which in this situation is the number of milliliters of the 75% solution that is to be added. We know that Pedro is going to add some amount so x must be more than 0 ml. Pedro cannot add more than the amount of 75% acid solution that he has in the lab.

4. What is a reasonable range for the situation?
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A reasonable range would be 15% to 75% 15% < f(x) < 75%
Notice that there are no equal signs. We know that Pedro is adding some amount so the 15% of the original solution will change. What he is adding is 75% acid, but the solution he is adding it to has a lesser amount of acid so he cannot actually get up to 75%. So, the percent of acid in the resulting solution must be between 15 and 75.