document.write( "Question 1121352: How many grams of pure silver must a silversmith mix with 100 grams of 55% silver alloy to produce 75% silver alloy? How many grams of 75% silver alloy will result? \n" ); document.write( "

Algebra.Com's Answer #737222 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "Here is a completely different way of solving mixture problems like this, where two \"ingredients\" are being mixed.

\n" ); document.write( "I find this method much easier and faster than the traditional algebraic method.

\n" ); document.write( "(1) Find where the percentage of the mixture (the final alloy, 75%) lies between the percentage of the original ingredient (55%) and the percentage of the ingredient being added (pure silver, 100%):
\n" ); document.write( "100-55 = 45
\n" ); document.write( "75-55 = 20
\n" ); document.write( "20/45 = 4/9

\n" ); document.write( "(2) The percentage of the final alloy is 4/9 of the way from 55% to 100%.

\n" ); document.write( "That means 4/9 of the mixture must be the ingredient that is being added.

\n" ); document.write( "So let 4x be the amount of the ingredient being added and 9x be the amount of the final alloy; that makes 5x the amount of the original alloy.

\n" ); document.write( "Since the amount of the original alloy was 100g, 5x=100g --> x=20g. So the amount of pure silver that needs to be added is 4x = 80g.

\n" ); document.write( "And the amount of the final alloy is 5x+4x = 9x = 180g. \n" ); document.write( "

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