document.write( "Question 1103821: A mixture of 8% disinfectant solution is to be made from 12% and 5% disinfectant solutions. How much of each solution should be used if 63 gallons of 8% solution are needed?
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Algebra.Com's Answer #718541 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Here is a method for solving mixture problems like this that is much faster and easier then the standard algebraic method usually shown.

\n" ); document.write( "The method uses a diagram like this:

\n" ); document.write( " $\"matrix%283%2C3%2C12%2C%22%22%2C3%2C%22%22%2C8%2C%22%22%2C5%2C%22%22%2C4%29\"$

\n" ); document.write( "The 12 and 5 in the first column are the percentages of the two ingredients.
\n" ); document.write( "The 8 in the middle column is the percentage of the mixture.
\n" ); document.write( "The 3 and 4 in the last column are the differences, computed diagonally, between the numbers in the first and second columns: 12-8=4; 8-5=3.

\n" ); document.write( "When the numbers given in the problem are used in this way, the numbers in the last column give the ratio in which the two ingredients need to be mixed.

\n" ); document.write( "In this problem, those numbers tell us that the 12% ingredient and the 5% ingredient need to be mixed in the ratio 3:4 to make an 8% mixture.

\n" ); document.write( "A ratio of 3:4 means 3/7 of the mixture should be the 12% solution and 4/7 should be the 5% solution. So
\n" ); document.write( "12%: 4/7 of 63 gallons = 36 gallons
\n" ); document.write( "5%: 3/7 of 63 gallons = 27 gallons \n" ); document.write( "

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