document.write( "Question 637707: A metallurgist needs to make 12.4 lbs. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use? \n" ); document.write( "

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A metallurgist needs to make 12.4 lbs. of an alloy containing 50% gold.
\n" ); document.write( " He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold.
\n" ); document.write( " How much of each should he use?
\n" ); document.write( ":
\n" ); document.write( "Common sense says that it would be half 50% alloy and half 40% alloy
\n" ); document.write( "But here is a the mixture equation
\n" ); document.write( ":
\n" ); document.write( "Let x = amt of 60% gold alloy required
\n" ); document.write( "the total is to be 12.4 lbs, therefore:
\n" ); document.write( "(12.4-x) = amt of 40% alloy required
\n" ); document.write( ":
\n" ); document.write( "Decimal equiv equation
\n" ); document.write( ".60x + .40(12.4-x) = .50(12.4)
\n" ); document.write( ".60x + 4.96 - .40x = 6.2
\n" ); document.write( ".60x - .40x = 6.2-4.96
\n" ); document.write( ".20x = 1.24
\n" ); document.write( "x = 1.24/.2
\n" ); document.write( "x = 6.2 lbs of the 60% alloy
\n" ); document.write( "then
\n" ); document.write( "12.4 - 6.2 = 6.2 lbs of 40% alloy
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this
\n" ); document.write( ".6(6.2) + .4(6.2) = .5(12.4)
\n" ); document.write( "3.72 + 2.48 = 6.2
\n" ); document.write( "6.2 = 6.2 \n" ); document.write( "

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