document.write( "Question 966297: The Gorgeous Gown Shop had a no-tax-added sale of dresses. Ginny was so excited that she bought n dresses at $n each, paying for them with several $20 bills. The change she received back was less than $10. How much change did she received? \n" ); document.write( "
Algebra.Com's Answer #590619 by Edwin McCravy(20056)\"\" \"About 
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document.write( "If she bought 10n dresses at $10n she would pay $100n² with $5n² 20s and get no\r\n" );
document.write( "change back.  So no change at all is less than $10, so 10n dresses at $10 with\r\n" );
document.write( "no change may be an acceptable solution.  You'll have to ask your teacher.\r\n" );
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document.write( "Now we show that if she bought 10n±k dresses, she'd get the same change back as\r\n" );
document.write( "if she bought k < 5 dresses.\r\n" );
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document.write( "Suppose the change she got from k < 5 dresses at $k per dress was $c.\r\n" );
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document.write( "Then \r\n" );
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document.write( " k²-20 = c where brackets indicate the greatest integer function.\r\n" );
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document.write( "(1)  k² = 20 + c\r\n" );
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document.write( "If she bought k±10n dresses, her change would be \r\n" );
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document.write( "(k±10n)^2-20  \r\n" );
document.write( "k2±20nk+100n^2-20[(k±10n)^2/20]\r\n" );
document.write( "k2±20(nk+5n^2-[(k+10n)^2/20])\r\n" );
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document.write( "If we add ±20(nk+5n^2-[(k+10n)^2/20]) to both sides of (1),\r\n" );
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document.write( "k^2 ± 20(nk+5n^2-[(k+10n)^2/20]) = c ± 20(nk+5n^2-[(k+10n)^2/20])\r\n" );
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document.write( "we have added or subtracted a whole number of $20 bills and so her \r\n" );
document.write( "change will still be $c\r\n" );
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document.write( "Let's assume she did get some change back. \r\n" );
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document.write( "If she bought 1 dress for $1 each, she'd get $20-$1=$19 change.  Not acceptable\r\n" );
document.write( "If she bought 2 dresses for $2 each, she'd get $20-$4=$16 change. Not acceptable\r\n" );
document.write( "If she bought 3 dresses for $3 each, she'd get $20-$9=$11 change. Not assceptable.\r\n" );
document.write( "If she bought 4 dresses for $4 each, she'd get $20-$16=$4. Acceptable!\r\n" );
document.write( "If she bought 5 dresses for $5 each, she'd get $40-$25=$15. Not acceptable.\r\n" );
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document.write( "Every other number of dresses differs from those by a multiple of 10 and thus\r\n" );
document.write( "has one of those same amounts of change.\r\n" );
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document.write( "The only possible amounts she can get in change are $19,$16,$11,$4,$15.\r\n" );
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document.write( "There are only two amounts she can get in change less than $10, $0 and $4.\r\n" );
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document.write( "If she must get back some change, then the only possible amount of change is $4.\r\n" );
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document.write( "Edwin
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