document.write( "Question 646752: If in the army there is one officer for every 16 privates, how many officers are there in a regiment consisting of 1,105 officers and privates? \n" ); document.write( "

Algebra.Com's Answer #852482 by ikleyn(53339) $\"\"$ $\"About$

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\n" ); document.write( "If in the army there is one officer for every 16 privates, how many officers are there in a regiment
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @Theo is incorrect and goes far out of the target.\r
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
\n" ); document.write( "\n" ); document.write( "        I will give two solutions: one arithmetic and other algebraic.\r
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document.write( "                Arithmetic solution\r\n" );
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document.write( "According to the problem we can group all people in groups, each containing 16 privates and 1 officer.\r\n" );
document.write( "So, each group is 17 people. The number of groups is 1105 divided by 17, which is\r\n" );
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document.write( "     = 65.\r\n" );
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document.write( "So, there 65 groups and, correspondingly, 65 officers.\r\n" );
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document.write( "ANSWER.  65 officers and  1105 - 65 = 1040 privates.\r\n" );
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document.write( "                Algebraic solution\r\n" );
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document.write( "Let x be the number of officers.  Then the number of privates is 16x, according to the problem.\r\n" );
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document.write( "Write an equation for the total\r\n" );
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document.write( "    x + 16x = 1105.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    17x = 1105,  x = 1105/17 = 65.\r\n" );
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document.write( "We get the same answer:  65 officers  and  1105 - 65 = 1040 privates.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, the problem is solved in two ways for your better understanding.\r
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\n" ); document.write( "\n" ); document.write( "The algebra solution is, actually, the same Arithmetic solution, retold using formulas instead of words.\r
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