document.write( "Question 160286: One alloy is one part copper to three parts tin. A second alloy is one part copper to four parts tin. How much of the second alloy should be combined with 24 pounds of the first alloy to obtain a new alloy that is two parts copper to seven parts tin? \n" ); document.write( "
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One alloy is one part copper to three parts tin. A second alloy is one part copper to four parts tin. How much of the second alloy should be combined with 24 pounds of the first alloy to obtain a new alloy that is two parts copper to seven parts tin?
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\n" ); document.write( "Let x = pounds of second alloy to be added
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\n" ); document.write( "From: \"One alloy is one part copper to three parts tin.\"
\n" ); document.write( "we know that:
\n" ); document.write( "total of four parts
\n" ); document.write( ".25 is copper
\n" ); document.write( ".75 is tin
\n" ); document.write( ".
\n" ); document.write( "From: \"A second alloy is one part copper to four parts tin.\"
\n" ); document.write( "total of four parts
\n" ); document.write( ".20 is copper
\n" ); document.write( ".80 is tin
\n" ); document.write( ".
\n" ); document.write( "We want:
\n" ); document.write( "2/9 copper
\n" ); document.write( "7/9 tin
\n" ); document.write( ".
\n" ); document.write( "Just consider the copper (we could have considered tin or copper -- didn't matter):
\n" ); document.write( ".25(24) + .20x = (2/9)(24+x)
\n" ); document.write( ".25(24) + .20x = (2/9)(24+x)
\n" ); document.write( "6 + .20x = (2/9)(24+x)
\n" ); document.write( "54 + 1.8x = (2)(24+x)
\n" ); document.write( "54 + 1.8x = 48+2x
\n" ); document.write( "6 = .2x
\n" ); document.write( "30 pounds = x
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