document.write( "Question 1203240: There are $925 in $5, $10, and $20 bills in a cash register. There is a total of 71 bills. The number of $20 bills is 7 less than the total number of $5 bills and $10 bills. How many bills of each denomination are in the cash register? \n" ); document.write( "

Algebra.Com's Answer #838656 by ikleyn(53765) $\"\"$ $\"About$

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\n" ); document.write( "There are $925 in $5, $10, and $20 bills in a cash register. There is a total of 71 bills.
\n" ); document.write( "The number of $20 bills is 7 less than the total number of $5 bills and $10 bills.
\n" ); document.write( "How many bills of each denomination are in the cash register?
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\n" ); document.write( "\n" ); document.write( " I will show you how to solve the problem
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document.write( "Let x be the number of the  5-dollar bills;\r\n" );
document.write( "Let y be the number of the 10-dollar bills.\r\n" );
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document.write( "Then the number of the 20-dollar bills is (x+y-7).\r\n" );
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document.write( "Write an equation for the total number of bills\r\n" );
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document.write( "    x + y + (x+y-7) = 71.\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "    2x + 2y = 71 + 7 = 78,\r\n" );
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document.write( "or\r\n" );
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document.write( "    x + y = 39.\r\n" );
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document.write( "Write second equation for the total money\r\n" );
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document.write( "    5x + 10y + 20(x+y-7) = 925.\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "     x + 2y + 4(x+y-7) = 185\r\n" );
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document.write( "     x + 2y + 4x + 4y - 28 = 185\r\n" );
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document.write( "    5x + 6y = 185 + 28 = 213\r\n" );
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document.write( "So, you have now the system of two equations\r\n" );
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document.write( "     x +  y =  39,    (1)\r\n" );
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document.write( "    5x + 6y = 213.    (2)\r\n" );
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document.write( "To solve it, multiply equation (1) by 5 (both sides); keep equation (2) as is.  You will get\r\n" );
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document.write( "    5x + 5y = 195,    (1')\r\n" );
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document.write( "    5x + 6y = 213.    (2')\r\n" );
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document.write( "Subtract equation (1') from equation (2').  You will get\r\n" );
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document.write( "    6y - 5y = 213 - 195\r\n" );
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document.write( "      y     =    18.\r\n" );
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document.write( "Now from equation (1)  x = 39-y = 39-18 = 21.\r\n" );
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document.write( "ANSWER.   There are 21 of the 5-dollar bills,  18 of the 10-dollar bills, and (x+y-7) = (21+18-7) = 32 of the 20-dollar bills.\r\n" );
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document.write( "CHECK.   21*5 + 18*10 + 32*20 = 925 dollars total.  ! correct !\r\n" );
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