document.write( "Question 1096295: We would like to share equally a sum of money between multiple people. If we give 20$ to each person there will be 40$ left over. If we give 25$ to each person there will be 75$ missing. How many people are there? \r
\n" ); document.write( "\n" ); document.write( "I don't understand this question in my homework and we are working on equations. Someone please help!\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #710736 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "We would like to share equally a sum of money between multiple people. If we give 20$ to each person there will be 40$ left over.
\n" ); document.write( "If we give 25$ to each person there will be 75$ $\"highlight%28cross%28missing%29%29\"$ short off. How many people are there?
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let N be the number of people, and let M be an amount of money (in dollars).\r\n" );
document.write( "\r\n" );
document.write( "The condition says \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "M = 20*N + 40    (1)   (\"If we give 20$ to each person there will be 40$ left over.\")\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The condition also says\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "M = 25*N - 75    (2)  (\"If we give 25$ to each person there will be 75$ short off.\")\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Left sides of equations (1) and (2) are the same.  Hence, their right sides are equal:\r\n" );
document.write( "\r\n" );
document.write( "20*N + 40 = 25*N - 75.    (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is your key/major equation. Solve it to find N:\r\n" );
document.write( "\r\n" );
document.write( "40 + 75 = 25N - 20N  ====>  5N = 115 ====>  N =  = 23.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There were 23 people and  M = 20*N + 40 = 20*23 + 40 = 500 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.  23*20 = 460 dollars,  and 40 dollars left.\r\n" );
document.write( "\r\n" );
document.write( "        23*25 = 575 dollars,  and 75 dollars short off.\r\n" );
document.write( "\r\n" );
document.write( "Answer.  There were 23 people and  500 dollars.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Their wording was not perfect (in my view), so I edited it, according to my common sense.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------------
\n" ); document.write( "If you want to see more similar problems solved, look in my lesson\r
\n" ); document.write( "\n" ); document.write( " - Had they sold . . .\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Happy learning ! !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );