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)![]() ![]() You can put this solution on YOUR website! . \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? \n" ); document.write( "~~~~~~~~~~~~~~~~~~\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( "Let x be the number of the luxury units;\r\n" ); document.write( "\r\n" ); document.write( " y be the number of the superior units.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Then the number of the deluxe units is 24 - x - y.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Assuming maximum accommodation (fulfillment) of the units, we write this equation\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " 8x + 7y + 5*(24-x-y) = 160.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "We simplify it\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " 8x + 7y + 120 - 5x - 5y = 160\r\n" ); document.write( "\r\n" ); document.write( " 3x + 2y = 160 - 120\r\n" ); document.write( "\r\n" ); document.write( " 3x + 2y = 40\r\n" ); document.write( "\r\n" ); document.write( " x =\r \n" ); document.write( "\n" ); document.write( "Solved.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-----------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "After reading my solution, do not forget to post your \"THANKS\" to me for my teaching.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "It is a Math Olympiad level, or a Math circle level problem.\r \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Come again to the forum soon to learn something new (!)\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |