document.write( "Question 1102691: The average age of boys in a class of 30 is 15 years. If 10 more boys join the class, the average of the whole class gets reduced by a year. What is the average age of newcomers? \n" ); document.write( "

Algebra.Com's Answer #717403 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "Since \"The average age of boys in a class of 30 is 15 years\", the sum of their ages is 30*15 = 450 years.\r\n" );
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document.write( "Let N be the average age of 10 newcomers.  Then the sum of their ages is 10N.\r\n" );
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document.write( "The total sum of 30 + 10 boys is 450 + 10N, and their average age is .\r\n" );
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document.write( "So, from the condition you have this equation\r\n" );
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document.write( " = (15-1) = 14.\r\n" );
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document.write( "Then  450 + 10N = 14*40 = 560  ====>  10N = 560 - 450 = 110  ====>  N =  = 11.\r\n" );
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document.write( "Answer.  The average age of newcomers is 11 years.\r\n" );
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document.write( "Check.    = 14.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Or even simpler logical analysis:\r
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document.write( "    Since \"The average age of boys in a class of 30 is 15 years\", the sum of their ages is 30*15 = 450 years.\r\n" );
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document.write( "    After joining 10 newcomers, the average age became 15-1 = 14 years;  hence, the sum of ages of all 40 students \r\n" );
document.write( "    of the class is 40*14 = 560 years now.\r\n" );
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document.write( "    The difference 560-450 = 110 years IS THE SUM of ages of the 10 newcomers.\r\n" );
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document.write( "    Hence, their average age is  = 11 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "You got the same answer.\r
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\n" ); document.write( "\n" ); document.write( "Surely, this \"logical analysis\" is the same solution, simply presented in the wording form.\r
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