document.write( "Question 1164209: Susan cashed a check at the bank, but the teller made a mistake. He gave her as many dollars as he should have given her cents and as many cents as he should have given her dollars. Susan took the money without realizing the error and spent $3.50. She then had twice as much money as the actual amount of the check. What was the amount of the check? \n" ); document.write( "
Algebra.Com's Answer #788660 by Edwin McCravy(20060) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "The other tutor's answer is correct, but he didn't really solve it.  He used\r\n" );
document.write( "trial and error.  Here is how to solve it completely, using no trial and\r\n" );
document.write( "error.  This is a \"Diophantine equation\", i.e. one that is solved only in\r\n" );
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document.write( "D = dollars\r\n" );
document.write( "C = cents\r\n" );
document.write( "100D + C = amount check was for (in pennies)\r\n" );
document.write( "100C + D = amount the teller gave Susan (in pennies)\r\n" );
document.write( "100C + D - 350 = how much she had after spending $3.50 (in pennies)\r\n" );
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document.write( "The cents can only be a 1 or 2 digit number, and since they were switched\r\n" );
document.write( "the dollars can also only be a 1 or 2 digit number. \r\n" );
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document.write( "So \r\n" );
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document.write( "That simplifies to\r\n" );
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document.write( "Solve for c\r\n" );
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document.write( "Isolate the fractions on the right:\r\n" );
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document.write( "The left side is an integer, so the right must also be\r\n" );
document.write( "that same integer.  Let that integer be A\r\n" );
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document.write( "Solve for d\r\n" );
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document.write( "Isolate fractions on the right\r\n" );
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document.write( "The left side is an integer, so the right must also be\r\n" );
document.write( "that same integer.  Let that integer be B.\r\n" );
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document.write( "Solve for A\r\n" );
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document.write( "Isolate the fraction on the right:\r\n" );
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document.write( "The left side is an integer, so \r\n" );
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document.write( "The left side is an integer, so the right must also be\r\n" );
document.write( "that same integer.  Let that integer be E (since we've\r\n" );
document.write( "used c and d).\r\n" );
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document.write( "Substitute 3E+1 for A and 2E for B in\r\n" );
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document.write( "We can tell that E=0, otherwise d would be more than a 2 digit number.\r\n" );
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document.write( "So E=0 and d = 98(0)+14 = 14\r\n" );
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document.write( "Substitute 0 for E in\r\n" );
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document.write( "Substitute 14 for d and A = 1 in\r\n" );
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document.write( "Therefore d=14 dollars and c = 32 cents.\r\n" );
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document.write( "The check was for $14.32.\r\n" );
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document.write( "Checking:  $32.14 - $3.50 = $28.64 which is twice $14.32\r\n" );
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document.write( "Edwin \n" );
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