document.write( "Question 1008375: If 5 men and 3 boys can reap 23 acres in 4 days and 3 men and 2 boys can reap 7 acres in 2 days , how many boys must assist 7 men in order that they may reap 45 acres in 6 days?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #624096 by ikleyn(52908) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "If 5 men and 3 boys can reap 23 acres in 4 days and 3 men and 2 boys can reap 7 acres in 2 days , how many boys must assist 7 men in order that they may reap 45 acres in 6 days?
\n" ); document.write( "-------------------------------------------------------------\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let m be (an unknown) rate of work for one man, measured in , \r\n" );
document.write( "and let b be (an unknown) rate of work for one boy, measured in same units.\r\n" );
document.write( "\r\n" );
document.write( "Then we have a system of two linear equations in two unknowns m and b\r\n" );
document.write( "\r\n" );
document.write( "4*(5m + 3b) = 23,   (1)\r\n" );
document.write( "2*(3m + 2b) =  7.   (2)\r\n" );
document.write( "\r\n" );
document.write( "Or\r\n" );
document.write( "\r\n" );
document.write( "20m + 12b = 23,     (1')\r\n" );
document.write( " 6m +  4b =  7.     (2')\r\n" );
document.write( "\r\n" );
document.write( "To solve it, multiply (2') by 3 and then distract it from (1'). You will get\r\n" );
document.write( "\r\n" );
document.write( "20m - 18m = 23 - 3*7, or\r\n" );
document.write( "\r\n" );
document.write( "2m = 2, hence, m = 1. \r\n" );
document.write( "\r\n" );
document.write( "Substitute it into (2'), and you will get 4b = 7 - 6 = 1, hence, b = .\r\n" );
document.write( "\r\n" );
document.write( "Thus you obtained that 1 man can reap 1 acr in 1 day, while 1 boy can reap  of acr in 1 day.\r\n" );
document.write( "\r\n" );
document.write( "Then 7 men in 6 days can reap 7*6*1 = 42 acres.\r\n" );
document.write( "\r\n" );
document.write( "How many boys must assist to reap remaining 45-42 = 3 acres acres in 6 days?\r\n" );
document.write( "\r\n" );
document.write( "Their number is  =  = 2.\r\n" );
document.write( "\r\n" );
document.write( "Answer. Two boys.\r\n" );
document.write( "

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

\n" );