document.write( "Question 182509: Solve using a system of equations (show the two equations you used then show the solutions):
\n" ); document.write( "A sofa and chair cost $850 as a set. If the sofa cost $100 more than twice as much as the chair what is the cost of each? \n" ); document.write( "

Algebra.Com's Answer #137138 by MathGuyJoe(20) $\"\"$ $\"About$

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Let x = cost of Sofa
\n" ); document.write( "Let y = cost of Chair
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\n" ); document.write( "The first statement: \"A sofa and chair cost $850 as a set\" gives us:
\n" ); document.write( "Equation 1: $\"+x+%2B+y+=+850+\"$
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\n" ); document.write( "The second statement: \"...the sofa cost $100 more than twice as much of the chair\" gives us:
\n" ); document.write( "Equation 2: $\"+x+=+100+%2B+2y+\"$
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\n" ); document.write( "Now, we can substitute $\"+%28100+%2B+2y%29+\"$ into the first equation (in place of x) to solve for the price of the Chair (y):
\n" ); document.write( " $\"+x+%2B+y+=+850+\"$ <- Equation 1
\n" ); document.write( " $\"+%28100+%2B+2y%29+%2B+y+=+850+\"$ <- substitute in for x
\n" ); document.write( " $\"+100+%2B+3y+=+850+\"$ <- group the y's
\n" ); document.write( " $\"+++++++3y+=+750+\"$ <- subtract 100 from both sides
\n" ); document.write( " $\"++++++++y+=+250+\"$ <- divide both sides by 3
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\n" ); document.write( "So the price for the Chair is $250. Looking at equation 1, that means the price of the Sofa must be $600.
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\n" ); document.write( "Hope this helps! ~ Joe \n" ); document.write( "

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