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...or you might want to see if this alternative method for solving mixture problems makes sense to you. If you understand it, it will take much less time and effort to solve this type of problem.
\n" ); document.write( "The key to this method is that the ratio in which the two ingredients must be mixed is exactly determined by how far the final percentage is from the percentages of the two ingredients.
\n" ); document.write( "The first thing you want to do with this method is decide whether you need more of ingredient A or ingredient B. In your example, the 8% of the final mixture is closer to 10% than it is to 5%, so you will need more of the 10% ingredient.
\n" ); document.write( "Now find the exact differences between the final mixture percentage and the percentages of the two ingredients. The ratio of those differences is the ratio in which the two ingredients need to be mixed.
\n" ); document.write( "10-8 = 2; 8-5 = 3; the ratio is 2:3. That means 2/5 of the 25 gallons must be one ingredient and 3/5 must be the other. And since we already determined that we need more of the 10% ingredient, we have the answer:
\n" ); document.write( "10% ingredient: 3/5 of 25 gallons = 15 gallons
\n" ); document.write( "5% ingredient: 2/5 of 25 gallons = 10 gallons
\n" ); document.write( "With all the words of explanation, it seems like a lot of work. But here is all that is really involved in solving the problem by this method:
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\n" ); document.write( "the ratio is 2:3; the fractions are 2/5 and 3/5.
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