document.write( "Question 170296This question is from textbook Introductory Algebra
\n" ); document.write( ": This is a story problem: A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelfths pure gold. How many ounces of each should be melted and mixed in order to obtain a 6-oz mixture that is two-thirds pure?
\n" ); document.write( "Could you please lead me in the right direction for solving this problem? \n" ); document.write( "
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This is a story problem: A goldsmith has two alloys that are different purities of gold. The first is three-fourths pure gold and the second is five-twelfths pure gold. How many ounces of each should be melted and mixed in order to obtain a 6-oz mixture that is two-thirds pure?
\n" ); document.write( "Could you please lead me in the right direction for solving this problem?
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\n" ); document.write( "In the first alloy, the gold is (3/4) of the alloy.
\n" ); document.write( "In the 2nd alloy, the gold is 5/12 of the alloy.
\n" ); document.write( "In the resulting alloy, 1/3 of 6 oz is gold, which is 4 oz.
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\n" ); document.write( "He can use x ounces of the 1st, and 6-x of the 2nd alloy.
\n" ); document.write( "So, x*(3/4) + (6-x)*(5/12) = 4
\n" ); document.write( "3x/4 + (6-x)*(5/12) = 4
\n" ); document.write( "Multiply by 12 to eliminate fractions
\n" ); document.write( "9x + 5*(6-x) = 48
\n" ); document.write( "9x + 30 -5x = 48
\n" ); document.write( "4x = 18
\n" ); document.write( "x = 4.5 (oz of the 1st alloy)
\n" ); document.write( "6-4.5 = 1.5 (oz of the 2nd alloy)\r
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