document.write( "Question 1169761: Some children share an amount of money equally and each of them gets $20. If the number of children sharing the same amount of money is reduced by 5, each child will get $40. Find the amount of money. \n" ); document.write( "

Algebra.Com's Answer #794614 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            For many students, such problems perplex them.\r
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\n" ); document.write( "\n" ); document.write( "            Surely, the most intriguing part is to setup them correctly.\r
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\n" ); document.write( "\n" ); document.write( "            Here I propose my version of setup and solution.\r
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document.write( "Let M be the amount of money: the unknown value under the problem's question.\r\n" );
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document.write( "In the basic scenario, the number of students is  .\r\n" );
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document.write( "In the hypothetical scenario  ( \" if \" ), the number of students is  .\r\n" );
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document.write( "The difference is 5, which gives you this equation\r\n" );
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document.write( "     -  = 5.\r\n" );
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document.write( "At this point, the setup is just done and completed.\r\n" );
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document.write( "The solution of the equation is in couple of lines.  Multiply both sides by 40.  You will get\r\n" );
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document.write( "    2M     -  M  = 5*40\r\n" );
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document.write( "         M       = 200.\r\n" );
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document.write( "ANSWER.  The amount of money is 200 dollars.\r\n" );
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document.write( "CHECK.    = 10 students;    = 5 students;   10-5 = 5 students,   which is PRECISELY CORRECT !\r\n" );
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\n" ); document.write( "\n" ); document.write( "When you solve it in this way, you feel a joy of getting mathematically beautiful solution (!)\r
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\n" ); document.write( "\n" ); document.write( "If you ask me for what purposes math teachers and textbooks give such problems to students, my answer would be\r
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\n" ); document.write( "\n" ); document.write( " \"such problems play very important role teaching students to distinct really beautiful Math problems from routine ones\r
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\n" ); document.write( "\n" ); document.write( " and really nice solutions from all the others.\"\r
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\n" ); document.write( "\n" ); document.write( "Therefore I so enthusiastically support and promote such problems at this forum.\r
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