document.write( "Question 1208420: Hi
\n" ); document.write( "The ratio of cows to sheep in farm X is 2 to 1 while that in farm Y is 3 to 1. Farm Y has twice as many cows and sheep as farm X. When 56 sheep are transferred from Y to X , the number of sheep in Y is 7/8 of the number of sheep in X.
\n" ); document.write( "Find the number of cows in Y.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #846829 by ikleyn(52818) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The ratio of cows to sheep in farm X is 2 to 1 while that in farm Y is 3 to 1.
\n" ); document.write( "Farm Y has twice as many cows and sheep altogether as farm X altogether.
\n" ); document.write( "When 56 sheep are transferred from Y to X , the number of sheep in Y is 7/8 of the number of sheep in X.
\n" ); document.write( "Find the number of cows in Y.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I edited your formulation by adding underlined words.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " In my opinion, it is necessary for better understanding and to make the text unambiguous.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let \"a\" be the number of sheep in farm X.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of cows in farm X is 2a.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At farm Y, the number of sheep is \"b\", and the number of cows is 3b.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Farm  Y  has twice as many cows and sheep  altogether as farm  X  altogether\r\n" );
document.write( "\r\n" );
document.write( "    b + 3b = 2(a+2a),\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    4b = 6a.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When 56 sheep are transferred from Y to X, the number of sheep at X is (a + 56);\r\n" );
document.write( "                                           the number of sheep at Y is (b - 56).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the number of sheep in Y is 7/8 of the number of sheep in X\r\n" );
document.write( "\r\n" );
document.write( "     = b-56.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify this equation\r\n" );
document.write( "\r\n" );
document.write( "    7(a+56) = 8*(b-56).\r\n" );
document.write( "\r\n" );
document.write( "    7a + 392 = 2*(4b) - 448.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the last equation, replace 4b by 6a, based on (1).  You will get\r\n" );
document.write( "\r\n" );
document.write( "    7a + 392 = 2*(6a) - 448\r\n" );
document.write( "\r\n" );
document.write( "    7a + 392 = 12a - 448\r\n" );
document.write( "\r\n" );
document.write( "    392 + 448 = 12a - 7a\r\n" );
document.write( "\r\n" );
document.write( "        840   = 5a\r\n" );
document.write( "\r\n" );
document.write( "          a   = 840/5 = 168.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now from (1) find  b =  =  = 252.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The number of cows in Y is  3b = 3*252 = 756.\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" ); document.write( "

\n" );