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 #788740 by MathTherapy(10555) $\"\"$ $\"About$

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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?
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Let amount of dollars and cents he should’ve given her be D, and C, respectively
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document.write( "Therefore, he should’ve given her: “100D + C” cents
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document.write( "Then, he gave her C dollars and D cents, or “100C + D” cents
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document.write( "She spent $3.50, or 350 cents
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document.write( "Therefore, we get: 100C + D - 350 = 2(100D + C)
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document.write( "100C + D - 350 = 200D + 2C
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document.write( "100C - 2C = 350 + 200D - D
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document.write( "98C = 350 + 199D
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document.write( "Converting this to a DIOPHANTINE EQUATION, we get: \r
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document.write( "Now, 2 * 98 = 196, and the integer that can be substituted for D in order to make 154 + 3D a DIVIDEND of 98 is 14. This gives us:  
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document.write( "So, with D being 14, we get: 
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document.write( "Therefore, D or number of dollars he should’ve given her was: 14, and number of cents he should’ve given her was: 32. Therefore, amount on check was:  \n" );
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