SOLUTION: A nurse has one solution that is 24% medicine and another that is 52% medicine. How much of the 52% solution must be added to the 30 milliliters of 24% solution to obtain a solutio

Question 1102899: A nurse has one solution that is 24% medicine and another that is 52% medicine. How much of the 52% solution must be added to the 30 milliliters of 24% solution to obtain a solution that is 40% medicine.
Found 2 solutions by jorel1380, greenestamps:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let n be the amount of 52% solution. Then:
30(.24)+n(.52)=.4(30+n)
7.2+.52n=12+.4n
.12n=4.8
n=40 ml of 52% solution
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Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The solution by the other tutor uses the standard algebraic method, which is perfectly good; it also is a good method for learning how to solve problems like this using algebra.

Here is what I think is a much faster and easier method to solve "mixture" problems like this. It uses the method of alligation, which is based on the ratios for mixing the two ingredients.

Here is what the diagram looks like for solving this problem using alligation.

The 24 and 52 in the first column are the given percentages of the two ingredients; the 40 in the middle of the figure is the percentage of the mixture.
The 12 and 16 in the last column are the differences, calculated diagonally, between the numbers in the first and second columns: 40-24=16, and 52-40=12.

With these calculations, the numbers in the last column represent the ratio in which the two ingredients need to be mixed. In this example, that ratio is 12:16, or 3:4.

So the ratio of the 24% solution to the 52% solution is 3:4; with 30ml of the 24% solution, you need 40ml of the 52% solution.
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