document.write( "Question 1209103: I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 400 pounds more than each of her trucks, but no more than 7/15 of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds? \n" ); document.write( "

Algebra.Com's Answer #847672 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "I own a large truck, and my neighbor owns four small trucks that are all identical.
\n" ); document.write( "My truck can carry a load of at least 400 pounds more than each of her trucks,
\n" ); document.write( "but no more than 7/15 of the total load her four trucks combined can carry.
\n" ); document.write( "Based on these facts, what is the greatest load I can be sure that my large truck
\n" ); document.write( "can carry, in pounds?
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\n" ); document.write( "\n" ); document.write( " It is a tangled problem.
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document.write( "Let \"m\" be the maximum load which my  track can carry, in pounds.\r\n" );
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document.write( "Let \"h\" be the maximum load which every her track can carry, in pounds.\r\n" );
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document.write( "The problem says \"My truck can carry a load of at least 400 pounds more than each of her trucks\".\r\n" );
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document.write( "It means that this inequality is true\r\n" );
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document.write( "    m >= h + 400.    (1)\r\n" );
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document.write( "Next, the problem says \"but no more than 7/15 of the total load her four trucks combined can carry\".\r\n" );
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document.write( "It means this inequality is true\r\n" );
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document.write( "    m <= .    (2)\r\n" );
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document.write( "For better visibility, let's rewrite inequalities (1) and (2) as one compound inequality\r\n" );
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document.write( "    h + 400 <= m <=     (3)\r\n" );
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document.write( "From this inequality (3), we conclude that THIS inequality is true\r\n" );
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document.write( "    h + 400 <= ,\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "    h + 400 <= .    (4)\r\n" );
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document.write( "We can easy solve it and evaluate \"h\" from the bottom.  For it, collect the terms with \"h\" on the right side,\r\n" );
document.write( "keeping the constant on the left side\r\n" );
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document.write( "    400 <=  - h,\r\n" );
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document.write( "    400 <= ,\r\n" );
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document.write( "     <= h,\r\n" );
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document.write( "     <= h,\r\n" );
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document.write( "    461 <= h,\r\n" );
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document.write( "    h >= 461.\r\n" );
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document.write( "Thus,  \"her\" truck can carry 461 pounds.\r\n" );
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document.write( "Hence,  \"my\" truck can carry 400 pounds more, i.e.  461 + 400 = 861 pounds.\r\n" );
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document.write( "ANSWER.  My car can carry 861 pounds, for sure.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus we untangled the problem and solved it completely to the end, as I promised.\r
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