document.write( "Question 982656: in a quiz game of 20 questions, each correct answer earns 5 points. Each incorrect answer reduces the score by 2 points. Omitted questions scored 0 points. Jana has a total score of 59 points. How many questions did she omit? \n" ); document.write( "

Algebra.Com's Answer #802600 by ikleyn(52946) $\"\"$ $\"About$

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\n" ); document.write( "in a quiz game of 20 questions, each correct answer earns 5 points.
\n" ); document.write( "Each incorrect answer reduces the score by 2 points. Omitted questions scored 0 points.
\n" ); document.write( "Jana has a total score of 59 points. How many questions did she omit?
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document.write( "Let x = #of correct;  y = # of incorrect;  z = # of omitted.\r\n" );
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document.write( "From the condition, we have these equations for integer numbers x, y, z\r\n" );
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document.write( "    x + y + z = 20           (1)\r\n" );
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document.write( "    5x - 2y   = 59           (2)\r\n" );
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document.write( "    x >= 0, y>= 0, z >= 0    (3)\r\n" );
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document.write( "From equation (2) and inequality y >= 0, we have  x >= 12.\r\n" );
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document.write( "Multiply equation (2) by 2 (both sides) and then add with equation (2).  You will get\r\n" );
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document.write( "    7x + 2z = 99,\r\n" );
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document.write( "          z = .      (4)\r\n" );
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document.write( "Now check, for which integer values of x from 12 to 13 inclusive you will have an integer value of z in formula (4).\r\n" );
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document.write( "The only such number of x is x = 13, giving z =  = 3\r\n" );
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document.write( "Then from equation (1)  y = 20 - 13 - 3 = 4.\r\n" );
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document.write( "ANSWER.  13 correct, 3 wrong and 4 omitted.\r\n" );
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