document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #717616 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "Here is what the diagram looks like for solving this problem using alligation.

\n" ); document.write( " $\"matrix%283%2C3%2C24%2C%22%22%2C12%2C%22%22%2C40%2C%22%22%2C52%2C%22%22%2C16%29\"$

\n" ); document.write( "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.
\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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. \n" ); document.write( "

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