document.write( "Question 1208202: Hi
\n" ); document.write( "There were 1081 visitors at a museum. 3/7 of the female visitors and 1/4 of the male visitors were children. If the number of female adults was 1/3 of the number of male adults, how many adult visitors were at the museum. \n" ); document.write( "

Algebra.Com's Answer #846464 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "There were 1081 visitors at a museum.
\n" ); document.write( "3/7 of the female visitors and 1/4 of the male visitors were children.
\n" ); document.write( "If the number of female adults was 1/3 of the number of male adults,
\n" ); document.write( "how many adult visitors were at the museum.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let 7x be the number of female visitors and 4y be the number of male visitors.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then 3x is the number of girls and 4x is the number of adult females;\r\n" );
document.write( "\r\n" );
document.write( "      y is the number of boys and 3y is the number of adult males.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equations:\r\n" );
document.write( "\r\n" );
document.write( "    7x + 4y = 1081,    (1)\r\n" );
document.write( "\r\n" );
document.write( "     = 4x,     (2)\r\n" );
document.write( "\r\n" );
document.write( "Equation (2) is the same as\r\n" );
document.write( "\r\n" );
document.write( "    y = 4x.           (2')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute (2') into (1)\r\n" );
document.write( "\r\n" );
document.write( "    7x + 4*(4x) = 1081\r\n" );
document.write( "\r\n" );
document.write( "    7x + 16x    = 1081\r\n" );
document.write( "\r\n" );
document.write( "      23x       = 1081\r\n" );
document.write( "\r\n" );
document.write( "        x       = 1081/23 = 47.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  y = 4*47 = 188.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER. The number of adult visitors was 4x + 3y = 4*47 + 3*188 = 752.\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" );