document.write( "Question 1179804: in a block of flats there are 24 units of 3 types: the luxury unit, the superior unit and deluxe unit. the luxury can accommodate 8 people, the superior unit can accommodate 7 people and deluxe can accommodate 5 people. given that the total number of people living in this block is 160. How many of each type are there? \n" ); document.write( "
Algebra.Com's Answer #809395 by ikleyn(52799)\"\" \"About 
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\n" ); document.write( "in a block of flats there are 24 units of 3 types: the luxury unit, the superior unit and deluxe unit.
\n" ); document.write( "The luxury can accommodate 8 people, the superior unit can accommodate 7 people and deluxe can accommodate 5 people.
\n" ); document.write( "Given that the total number of people living in this block is 160, how many of each type are there?
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document.write( "Let x be the number of the luxury units;\r\n" );
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document.write( "    y be the number of the superior units.\r\n" );
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document.write( "Then the number of the deluxe units is 24 - x - y.\r\n" );
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document.write( "Assuming maximum accommodation (fulfillment) of the units, we write this equation\r\n" );
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document.write( "    8x + 7y + 5*(24-x-y) = 160.\r\n" );
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document.write( "We simplify it\r\n" );
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document.write( "    8x + 7y + 120 - 5x - 5y = 160\r\n" );
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document.write( "    3x + 2y = 160 - 120\r\n" );
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document.write( "    3x + 2y = 40\r\n" );
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document.write( "     x      = \"%2840-2y%29%2F3\".\r\n" );
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document.write( "We want have x and y as integer numbers.  It gives for  x  and  y  these values  (see the TABLE)\r\n" );
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document.write( "    T    A    B    L    E\r\n" );
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document.write( "     x        y        z\r\n" );
document.write( "  luxury   superior   deluxe\r\n" );
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document.write( "     12       2       10\r\n" );
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document.write( "     10       5        9\r\n" );
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document.write( "      8       8        8\r\n" );
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document.write( "      6      11        7\r\n" );
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document.write( "      4      14        6\r\n" );
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document.write( "      2      17        5\r\n" );
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document.write( "      0      20        4\r\n" );
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document.write( "In parallel, we fill the column for z = 24 - x - y.\r\n" );
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document.write( "We do it until we have non-negative values for x, y, and z.\r\n" );
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document.write( "This list in the table is the FULL SET of all possible solutions to the given problem.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "After reading my solution,  do not forget to post your  \"THANKS\"  to me for my teaching.\r
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\n" ); document.write( "\n" ); document.write( "It is a  Math  Olympiad level,  or a  Math circle level problem.\r
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\n" ); document.write( "\n" ); document.write( "So,  feel yourself as if you visited a  Math circle session today,  and as if  I  was your mentor.\r
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\n" ); document.write( "\n" ); document.write( "Come again to the forum soon to learn something new (!)\r
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