document.write( "Question 1177662: The verbiage in this question is confusing me so much that I don't even know where to start. Any help in explaining and solving would be greatly appreciated. \r
\n" ); document.write( "\n" ); document.write( "The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014. Set up a system and then solve using technology. \r
\n" ); document.write( "\n" ); document.write( "// The table shows:\r
\n" ); document.write( "\n" ); document.write( "Airline ==> United Continental - American - Jet Blue - Southwest
\n" ); document.write( "Cost(in cents)==> 14.9, 14.6, 11.9, 12.4\r
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\n" ); document.write( "\n" ); document.write( "Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 235 empty seats, costing them a total of $99,060. If United Continental had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight? \n" ); document.write( "

Algebra.Com's Answer #850420 by ikleyn(52756) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        As the problem is solved in the post by @CPhill, it is one of possible ways/methods,\r
\n" ); document.write( "\n" ); document.write( "        but there is another, much more effective and more impressive way to solve the problem \r
\n" ); document.write( "\n" ); document.write( "        using only one equation from the very beginning, instead of three.\r
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\n" ); document.write( "\n" ); document.write( "        Also, it is worth to notice one very important fact:\r
\n" ); document.write( "\n" ); document.write( "        in the problem the information about 4 companies is given, but actually only three \r
\n" ); document.write( "\n" ); document.write( "        companies participate in the game. The fourth company, Jet Blue, is introduced\r
\n" ); document.write( "\n" ); document.write( "        and does present only to confuse the reader and to distract attention.\r
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document.write( "Let x be the number of empty seats for American.\r\n" );
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document.write( "Then the number of empty seats for United Continental is 3x,\r\n" );
document.write( "and the number of empty seats for Southwest is (235 - x - 3x) = 235 - 4x.\r\n" );
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document.write( "Now write the total cost equation for empty seats\r\n" );
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document.write( "    United Cont.        American        Southwest\r\n" );
document.write( "    3000*0.149*(3x)  +  3000*0.146*x  + 3000*0.124*(235-4x) = 99060  dollars.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "     1341x            + 438x          + 87420 - 1488x  = 99060\r\n" );
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document.write( "                        291x                           = 99060 - 87420 = 11640.\r\n" );
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document.write( "                           x                           = 11640/191 = 40.\r\n" );
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document.write( "So, the number of empty seats for American is 40;  for United Continental  3*40 = 120,\r\n" );
document.write( "                          and for Southwest 235-4*40 = 75.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Notice that in this solution the system of three equations is not even mentioned.\r
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