document.write( "Question 1074575: Holly is selling, goldfish, birds, and rabbits. Goldfish are $1, birds are $5, and rabbits are $10. She has 16 animals in total. If she sells all of them she will earn $99. The number of goldfish plus the number of birds is 2 more than the number of rabbits. How many of each animal does she have? \n" ); document.write( "

Algebra.Com's Answer #689222 by ikleyn(52812) $\"\"$ $\"About$

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\n" ); document.write( "Holly is selling, goldfish, birds, and rabbits. Goldfish are $1, birds are $5, and rabbits are $10. She has 16 animals in total.
\n" ); document.write( "If she sells all of them she will earn $99.
\n" ); document.write( "The number of goldfish plus the number of birds is 2 more than the number of rabbits.
\n" ); document.write( "How many of each animal does she have?
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document.write( "Let G be the number of goldfish and B be the number of birds.\r\n" );
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document.write( "Then the number of rabbits is G + B -2.\r\n" );
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document.write( "Thus we have these equations:\r\n" );
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document.write( "G + B + (G+B-2) = 16        (1)    (the number of animals in total)\r\n" );
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document.write( "G + 5B + 10*(G+B-2) = 99    (2)    (dollars; the total cost)\r\n" );
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document.write( "You have 2 equations for 2 unknowns. Simplify and write is the standard form:\r\n" );
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document.write( " 2G +  2B =  18             (1')\r\n" );
document.write( "11G + 15B = 119             (2')\r\n" );
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document.write( "Or even simpler\r\n" );
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document.write( "  G  +  B =   9             (1'')\r\n" );
document.write( "11G + 15B = 119             (2'')\r\n" );
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document.write( "Now express G = 9-B from (1'') and substitute it into (2''). You will get\r\n" );
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document.write( "11(9-B) + 15B = 119,   or\r\n" );
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document.write( "99 - 11B + 15B = 119,   or\r\n" );
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document.write( "4B = 119-99 = 20,   --->  B =  = 5.\r\n" );
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document.write( "Thus there are 5 birds.\r\n" );
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document.write( "Then the number of goldfish is  G = 9 - B = 4,\r\n" );
document.write( "and the number of rabbits is  G + B - 2 = 4 + 5 - 2 = 7.\r\n" );
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document.write( "Answer.  4 goldfish, 5 birds and 7 rabbits.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Lessons to learn from this solution:\r
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\n" ); document.write( "\n" ); document.write( "    - Chose the unknowns by a rational way;
\n" ); document.write( "    - write the system;
\n" ); document.write( "    - solve the system (I used the substitution method).\r
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