document.write( "Question 1096872: Ms. Nguyen is in debt to her mother, her brother, and her sister, for a total of $410. She owes her brother $10 less than five times what she owes her mother. She owes her sister $35 more than she does her mother. How much money does she owe to each? Define a variable, then write and solve an equation. To check your answer, make sure that the sum of her three debts is still $410. \n" ); document.write( "

Algebra.Com's Answer #711323 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "Let M be the amount Ms. Nguen is in debt to her mother (in dollars).\r\n" );
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document.write( "Then the amount Ms. Nguen is in debt to her brother is 5M-10 dollars.\r\n" );
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document.write( "Also, the amount Ms. Nguen is in debt to her sister is (M + 35) dollars.\r\n" );
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document.write( "In all,\r\n" );
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document.write( "M + (5M-10) + (M+35) = 410.      (1)\r\n" );
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document.write( "So, M is your variable and (1) is your equation.\r\n" );
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document.write( "To solve it, simplify\r\n" );
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document.write( "7M + 25 = 410  ====>  7M = 410-25 = 395  ====>  M =  = 55 dollars.\r\n" );
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document.write( "Answer.  The debt to the mother is $55.  The debt to the brother is 5*55-10 = $265.  The debt to the sister is 55+35 = $90.  \r\n" );
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document.write( "Check.   55 + 265 + 90 = 410 dollars.  ! Correct !\r\n" );
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