document.write( "Question 1139504: I think this is a system of equations question. \r
\n" ); document.write( "\n" ); document.write( "A farmer plants soybeans, corn, and wheat and rotates the planting each year on his 500 acre farm. In a particular year, the profits from his crops were $120 per acre of soybeans, $100 per acre of corn, and $80 per acre of wheat. He plants twice as many acres of corn as soybeans.\r
\n" ); document.write( "\n" ); document.write( "How many acres did he plant with each crop the year he made a total profit of $51,000? \n" ); document.write( "

Algebra.Com's Answer #759975 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( " $\"highlight%28cross%28I_think_this_is_a_system_of_equations_question%29%29\"$ . \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A farmer plants soybeans, corn, and wheat and rotates the planting each year on his 500 acre farm.
\n" ); document.write( "In a particular year, the profits from his crops were $120 per acre of soybeans, $100 per acre of corn, and $80 per acre of wheat.
\n" ); document.write( "He plants twice as many acres of corn as soybeans.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "How many acres did he plant with each crop the year he made a total profit of $51,000?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " This problem is to be solved using one equation in one single unknown.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the area for soybeans (in acres).\r\n" );
document.write( "\r\n" );
document.write( "Then the area for corn is  (2x)  acres, and the area for wheat is the rest  (500-x-2x) = (500-3x) acres.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "His total profit is then\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    120x + 100*(2x) + 80*(500-3x) = 51000   dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve for x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    120x + 200x + 40000 - 240x = 51000\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    80x                        = 51000 - 40000\r\n" );
document.write( "\r\n" );
document.write( "    80x                        = 11000\r\n" );
document.write( "\r\n" );
document.write( "      x                        =  = 137.5\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  137.5 acres for soybeans;  twice of it, 2*137.5 = 275 acres for corn,  and the rest, 500 - 137.5 - 275 = 87.5 acres for wheat.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, explained and completed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Advanced word problems to solve using a single linear equation\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO algebreze and solve these problems using one equation in one unknown \r
\n" ); document.write( "\n" ); document.write( "    - Challenging word problems to solve using a single linear equation \r
\n" ); document.write( "\n" ); document.write( "in this site, and learn the subject from there.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The major lesson to learn from my post is THIS :\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    This problem is designed, is intended, and is expected to be solved using one equation in one single unknown.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do not forget to post me your \"THANKS\" after reading my post ! \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );