A druggist needs to prepare 100ml. of a 10% solution. She has available only a 5% and a 25% solution. How much of each should she use to prepare the desired solution?

25 milliliters of 25% solution and 75 milliliters of 5% solution should be used.

Step-by-step explanation:

Since the druggist has to prepare 100 ml of a 10% solution, but has only 5% and 25% solutions, to determine the proportion of each solution that he must use to prepare the solution with the desired percentage, it is necessary to perform the following calculation:

25 x 1 + 5 x 0 = 25

25 x 0.9 + 5 x 0.1 = 23

25 x 0.8 + 5 x 0.2 = 21

25 x 0.7 + 5 x 0.3 = 19

25 x 0.6 + 5 x 0.4 = 17

25 x 0.5 + 5 x 0.5 = 15

25 x 0.4 + 5 x 0.6 = 13

25 x 0.3 + 5 x 0.7 = 11

25 x 0.2 + 5 x 0.8 = 9

Therefore, the percentage that the druggist must use will be between 20% and 30% of the 25% solution, and between 70% and 80% of the 5% solution, that is:

25 x 0.25 + 5 x 0.75 = 10

Therefore, the druggist should use a 25% solution at 25%, and a 75% solution at 5%: Thus, since 100 x 0.25 is equal to 25, 25 milliliters of 25% solution and 75 milliliters of 5% solution should be used.