document.write( "Question 98759This question is from textbook Mathematics Applications and Concepts
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document.write( "Number 8:  Number theory from Mixed Problem Solving\r
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document.write( "Find 2 numbers whose sum is 56 and whose product is 783.\r
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document.write( "What is asked in the problem?
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document.write( " Find 2 numbers whose sum is 56 and whose product is 783.\r
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document.write( "Representation:
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document.write( " Let x be the first number
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document.write( "     y be the second number\r
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document.write( "Equation:
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document.write( " x + y = 56   (1st equation)
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document.write( "    xy = 783  (2nd equation)\r
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document.write( "Solve the 2 equations, solve for x in terms of y using the first equation
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document.write( "   x + y = 56
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document.write( "       x = 56 - y\r
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document.write( "Substitute x to the second equation
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document.write( "              xy = 783, where x = 56 - y
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document.write( "      56 - y (y) = 783
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document.write( "    56(y) - y(y) = 783
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document.write( "       56y - y^2 = 783
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document.write( "               0 = y^2 - 56y + 783
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document.write( " Factor the equation y^2 - 56y + 783 = 0 to find the value of y.\r
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document.write( "            0 = y^2 - 56y + 783
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document.write( "            0 = (y - 29)(y - 27) 
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document.write( "            0 = y - 29    0 = y - 27
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document.write( "            y = 29        y = 27\r
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document.write( "There are 2 values for y. Substitute the values to either 
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document.write( "of the two equations for find values of x.\r
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document.write( "     x + y = 56, if y = 29
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document.write( "    x + 29 = 56
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document.write( "         x = 56 - 29
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document.write( "         x = 27\r
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document.write( "     x + y = 56, if y = 27     
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document.write( "    x + 27 = 56
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document.write( "         x = 56 - 27
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document.write( "         x = 29\r
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document.write( "Therefore if x = 29, y = 27. 
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document.write( "          if x = 27, y = 29.
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document.write( "There are two possibilities with the given problem. 
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