document.write( "Question 1172818: Tickets in the ocean park cost 500$ for adults and 400$ for children. The management collected a total amount of not more than 80 000$ from 120 adults and children. What are the possible number of adults and children in the Ocean Park? (find the inequality then GRAPH) \n" ); document.write( "

Algebra.Com's Answer #797957 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "This problem is a SPECIAL CASE: one equation is combined with one inequality.\r\n" );
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document.write( "The equation is\r\n" );
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document.write( "    x + y = 120.    (x for adults, y for children)\r\n" );
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document.write( "The inequality is\r\n" );
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document.write( "    500x + 400y <= 80000\r\n" );
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document.write( "Simplify this inequality by dividing both sides by 100\r\n" );
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document.write( "    5x + 4y <= 800.\r\n" );
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document.write( "So, you have, actually, this system (one equation and one inequality)\r\n" );
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document.write( "     x +  y  = 120\r\n" );
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document.write( "    5x + 4y <= 800\r\n" );
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document.write( "Also, the problem assumes that both quantities x and y are NON-NEGATIVE\r\n" );
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document.write( "    x >= 0,  y >= 0.\r\n" );
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document.write( "On the plot, it looks like this\r\n" );
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document.write( "    \r\n" );
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document.write( "     Plot y = 120-x (red line) and y =   (green line)\r\n" );
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document.write( "The inequality represents all the points inside the triangle in QI under the green line.\r\n" );
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document.write( "The equation represents the red line.\r\n" );
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document.write( "So, the range for x is  0 <= x <= 120.\r\n" );
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document.write( "    The range for y is the same 0 <= y <= 120.\r\n" );
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document.write( "But x and y are not independent variables: they are interconnected by the equation x + y = 120.\r\n" );
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document.write( "This plot allows you to see the problem in whole and its solution, in particular.\r\n" );
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document.write( "The solution set is { the INTEGER points of the red line in QI }.\r\n" );
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