document.write( "Question 1102836: Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90. How many dimes and how many quarters does she have? Write an equation for this situation and use it to solve the problem. [Hint: Use the decimal values of the \"c\" coins to write an equation.] \n" ); document.write( "

Algebra.Com's Answer #717546 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "The condition seems to be SUSPICIOUS, since it imposes 3 (three, THREE) conditions on 2 unknowns.\r
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document.write( "d + q = 61     (1)    (counting coins)\r\n" );
document.write( "q = d + 3      (2)    (\"3 more quarters than dimes\")\r\n" );
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document.write( "Substitute (2) into eq(1). You will get\r\n" );
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document.write( "d + (d+3) = 61  ====>  2d + 3 = 61  ====>  2d = 61-3 = 58  ====>  d =  = 29.\r\n" );
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document.write( "Answer.  Working with the first two parts of the condition (with TWO of the THREE), we get this answer:\r\n" );
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document.write( "         29 dimes and 29+3 = 32 quarters.\r\n" );
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document.write( "Now, let us check if the LAST condition is satisfied.\r\n" );
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document.write( "Total value = 29*10 + 32*25 = 1090.\r\n" );
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document.write( "Happily, the third condition is satisfied, so the solution and the problem itself are OK.\r\n" );
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document.write( "But still keep in mind that ONE OF THE THREE CONDITIONS is excessive and unnecessary.\r\n" );
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document.write( "The third condition is a potential source for the condition to be WRONG,\r\n" );
document.write( "but happily it is not the case here.\r\n" );
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