document.write( "Question 146437: Anne and Nancy use a metal alloy that is 19.75% copper to make jewalry. How many ounces of an 18% alloy must be mixed with a 21% alloy to form 108 ounces of the desired alloy? \n" ); document.write( "

Algebra.Com's Answer #106904 by nerdybill(7384) $\"\"$ $\"About$

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Anne and Nancy use a metal alloy that is 19.75% copper to make jewalry. How many ounces of an 18% alloy must be mixed with a 21% alloy to form 108 ounces of the desired alloy?
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\n" ); document.write( "Let x = ounces of 18% copper
\n" ); document.write( "and y = ounces of 21% copper
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\n" ); document.write( "since we have two unknowns, we need two equations.
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\n" ); document.write( "from:\"use a metal alloy that is 19.75% copper\" we get equation 1:
\n" ); document.write( ".18x + .21y = 19.75
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\n" ); document.write( "from:\"form 108 ounces of desired alloy\" we get equation 2:
\n" ); document.write( "x + y = 108
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\n" ); document.write( "Solve equation 2 for x we get:
\n" ); document.write( "x + y = 108
\n" ); document.write( "x = 108 - y
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\n" ); document.write( "Substitute this into equation 1 and solve for y:
\n" ); document.write( ".18x + .21y = 19.75
\n" ); document.write( ".18(108 - y) + .21y = 19.75
\n" ); document.write( ".18(108 - y) + .21y = 19.75
\n" ); document.write( "19.44 - .18y + .21y = 19.75
\n" ); document.write( "19.44 + .03y = 19.75
\n" ); document.write( ".03y = .31
\n" ); document.write( "y = 10.3333 (10 and 1/3) ounces
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\n" ); document.write( "substitute the above into equation 2 and solve for x:
\n" ); document.write( "x + y = 108
\n" ); document.write( "x + 10.333 = 108
\n" ); document.write( "x = 108 - 10.333
\n" ); document.write( "x = 97.667 (97 and 2/3) ounces
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