document.write( "Question 1154226: I can’t find the answer...\r
\n" ); document.write( "\n" ); document.write( "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 $800$ pounds more than each of her trucks, but no more than $\frac{1}{3}$ 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 #776633 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\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 800 pounds more than each of her trucks,
\n" ); document.write( "but no more than 1/3 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 can carry, in pounds?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The condition tells us these two facts\r\n" );
document.write( "\r\n" );
document.write( "    M >= H + 800       (1)\r\n" );
document.write( "\r\n" );
document.write( "    M <= .        (2)\r\n" );
document.write( "\r\n" );
document.write( "where M is \"my\" truck and H is \"her\" truck.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Or, in compound form\r\n" );
document.write( "\r\n" );
document.write( "    H + 800 <= M <= .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies\r\n" );
document.write( "\r\n" );
document.write( "    H + 800 <= .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify by multiplying by 3 (both sides)\r\n" );
document.write( "\r\n" );
document.write( "    3H + 2400 <= 4H\r\n" );
document.write( "\r\n" );
document.write( "Hence,\r\n" );
document.write( "\r\n" );
document.write( "    H >= 2400\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from (1)\r\n" );
document.write( "\r\n" );
document.write( "    M >= H + 800 = 2400 + 800 = 3200 pounds.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  3200 pounds is that greatest load \"I\" can be sure . . . \r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );