document.write( "Question 119100: When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient in terms of q, is\r
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Algebra.Com's Answer #87206 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the
\n" ); document.write( "quotient in terms of q, is
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\n" ); document.write( "i am really confuse about how to go about solving this. Thank you very much for your help.
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document.write( "You just have to know how to check a division problem like\r\n" );
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document.write( "           QUOTIENT \r\n" );
document.write( "DIVISOR)   DIVIDEND\r\n" );
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document.write( "          ___    \r\n" );
document.write( "          REMAINDER \r\n" );
document.write( "            \r\n" );
document.write( "that you multiply the QUOTIENT by the DIVISOR and then add the\r\n" );
document.write( "REMAINDER.  Then what you get must equal to the DIVIDEND.  \r\n" );
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document.write( "For instance, when the positive integer 57 is divided by 6,\r\n" );
document.write( "the quotient is 57 and the remainder is 5\r\n" );
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document.write( "   57\r\n" );
document.write( "6)347\r\n" );
document.write( "  30\r\n" );
document.write( "   47\r\n" );
document.write( "   42\r\n" );
document.write( "    5\r\n" );
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document.write( "To check the above: \r\n" );
document.write( "we multiply the quotient 57 by the divisor 6, getting 342.  Then\r\n" );
document.write( "we add the remainder, 5, to 342 and we get 347, which is equal \r\n" );
document.write( "to the dividend.\r\n" );
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document.write( "Now, using that information, taking your first sentence:\r\n" );
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document.write( ">>...When the positive integer n is divided by 7, the quotient \r\n" );
document.write( "is q and the remainder is 4...<<\r\n" );
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document.write( "      q  \r\n" );
document.write( "   7) n\r\n" );
document.write( "     __\r\n" );
document.write( "      4\r\n" );
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document.write( "So if we wanted to check that division as we did the numerical\r\n" );
document.write( "one, we would multiply the quotient q by the divisor 7, getting\r\n" );
document.write( "7q.  Then we would add the remainder, 4, to 7q and we'd get 7q+4,\r\n" );
document.write( "which would be equal to the dividend n.  So we would have the \r\n" );
document.write( "equation:\r\n" );
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document.write( "   7q+4 = n  \r\n" );
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document.write( "Your second sentence says:\r\n" );
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document.write( ">>...When 2n is divided by 7, the remainder is 1 and the \r\n" );
document.write( "quotient...is ____...<< \r\n" );
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document.write( "Let's let the quotient be x. Then we have:\r\n" );
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document.write( "      x  \r\n" );
document.write( "   7)2n\r\n" );
document.write( "     __\r\n" );
document.write( "      1\r\n" );
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document.write( "So if we wanted to check that division, we would multiply the\r\n" );
document.write( "quotient x by the divisor 7, getting 7x.  Then we would add the \r\n" );
document.write( "remainder, 1, to 7x and we get 7x+1, which would be equal to the \r\n" );
document.write( "dividend 2n.  So we would have the equation:\r\n" );
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document.write( "   7x+1 = 2n \r\n" );
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document.write( "The words I left out of the second sentence were \r\n" );
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document.write( ">>...in terms of q,...<<\r\n" );
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document.write( "So we have the two equations \r\n" );
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document.write( "   7q+4 = n\r\n" );
document.write( "   7x+1 = 2n\r\n" );
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document.write( "to solve for x the quotient, by substituting (7q+4) \r\n" );
document.write( "for n, gotten from the first equation, into the \r\n" );
document.write( "second equation:\r\n" );
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document.write( "   7x+1 = 2n\r\n" );
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document.write( "Rplace n by (7q+4)\r\n" );
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document.write( "   7x+1 = 2(7q+4)\r\n" );
document.write( "   \r\n" );
document.write( "then solving for x:\r\n" );
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document.write( "   7x+1 = 14q+8 \r\n" );
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document.write( "Add -1 to both sides\r\n" );
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document.write( "     7x = 14q+8-1\r\n" );
document.write( "     7x = 14q+7\r\n" );
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document.write( "Divide every term on both sides by 7\r\n" );
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document.write( "     =  + \r\n" );
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document.write( "      x = 2q+1\r\n" );
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document.write( "So the correct answer is (d).\r\n" );
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document.write( "Edwin

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