document.write( "Question 663902: At the 2006 Winter Olympics in Italy, the top medal winner was Germany, which won a total of 29 medals. Germany won 1 more silver medal than gold and 5 more gold medals than bronze. Find the number of each type of medal won. How do I solve this? \n" ); document.write( "
Algebra.Com's Answer #852493 by ikleyn(52969)\"\" \"About 
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\n" ); document.write( "At the 2006 Winter Olympics in Italy, the top medal winner was Germany, which won a total of 29 medals.
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\n" ); document.write( "Find the number of each type of medal won. How do I solve this?
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\n" ); document.write( "\n" ); document.write( "        Tutor @Theo provided long wordy solution with a lot of unnecessary complications.\r
\n" ); document.write( "\n" ); document.write( "        I will give here much shorter solution, which I hope is more clear, more accessible and more instructive.\r
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document.write( "Let x be the number of gold medals Germany won.\r\n" );
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document.write( "Then the number of silver medals is (x+1), according to the problem,\r\n" );
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document.write( "and the number of bronze medals was ((x-5).\r\n" );
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document.write( "Write an equation expressing the total number of medals\r\n" );
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document.write( "    x + (x+1) + (x-5) = 29   (29 in the right side is the given total).\r\n" );
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document.write( "Simplify collecting and combining like terms\r\n" );
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document.write( "    3x - 4 = 29,\r\n" );
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document.write( "    3x = 29 + 4,\r\n" );
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document.write( "    3x = 33,\r\n" );
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document.write( "     x = 33/3 = 11.\r\n" );
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document.write( "So, the number of gold medals was 11;  the number of silver medals was 11+1 = 121;  the number of bronze medals was 11-5 = 6.\r\n" );
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document.write( "CHECK.  The total is  11 + 12 + 6 = 29.   ! correct !\r\n" );
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