document.write( "Question 1175417: A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.35 per ounce? \n" ); document.write( "

Algebra.Com's Answer #801014 by VFBundy(438) $\"\"$ $\"About$

You can put this solution on YOUR website!
Ounces of $4.30 alloy = x
\n" ); document.write( "Ounces of $1.80 alloy = y
\n" ); document.write( "
\n" ); document.write( "Make two equations:
\n" ); document.write( "
\n" ); document.write( "x + y = 200
\n" ); document.write( "4.30x + 1.80y = 200(2.35)
\n" ); document.write( "
\n" ); document.write( "Simplify second equation:
\n" ); document.write( "
\n" ); document.write( "4.30x + 1.80y = 470
\n" ); document.write( "
\n" ); document.write( "Here are your two equations:
\n" ); document.write( "
\n" ); document.write( "x + y = 200
\n" ); document.write( "4.30x + 1.80y = 470
\n" ); document.write( "
\n" ); document.write( "Multiply first equation by -1.80:
\n" ); document.write( "
\n" ); document.write( "-1.80x - 1.80y = -360
\n" ); document.write( "
\n" ); document.write( "Here are your two equations:
\n" ); document.write( "
\n" ); document.write( "-1.80x - 1.80y = -360
\n" ); document.write( "4.30x + 1.80y = 470
\n" ); document.write( "
\n" ); document.write( "Add both equations together:
\n" ); document.write( "
\n" ); document.write( "2.50x = 110
\n" ); document.write( "
\n" ); document.write( "Solve for x:
\n" ); document.write( "
\n" ); document.write( "x = 44
\n" ); document.write( "
\n" ); document.write( "Plug x = 44 into the original first equation to find y:
\n" ); document.write( "
\n" ); document.write( "x + y = 200
\n" ); document.write( "
\n" ); document.write( "44 + y = 200
\n" ); document.write( "
\n" ); document.write( "y = 156
\n" ); document.write( "
\n" ); document.write( "Ounces of $4.30 alloy = x = 44
\n" ); document.write( "Ounces of $1.80 alloy = y = 156 \n" ); document.write( "

\n" );