Question 182509
Let x = cost of Sofa
Let y = cost of Chair
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The first statement:  "A sofa and chair cost $850 as a set" gives us:
<u>Equation 1:</u>  {{{ x + y = 850 }}}
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The second statement: "...the sofa cost $100 more than twice as much of the chair" gives us:
<u>Equation 2:</u>  {{{ x = 100 + 2y }}}
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Now, we can substitute {{{ (100 + 2y) }}} into the first equation (in place of x) to solve for the price of the Chair (y):
{{{ x + y = 850 }}} <- Equation 1
{{{ (100 + 2y) + y = 850 }}} <- substitute in for x
{{{ 100 + 3y = 850 }}} <- group the y's
{{{       3y = 750 }}} <- subtract 100 from both sides
{{{        y = 250 }}} <- divide both sides by 3
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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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Hope this helps! ~ Joe