document.write( "Question 1123330: Fundraising. The Buck Creek Fire Department served 250 dinners. A child’s plate cost $5.50 and an adult’s plate cost $9.00. A total of $1935 was collected. How many of each type of plate were served? \n" ); document.write( "

Algebra.Com's Answer #739628 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "One approach is to solve the system of two equations in two unknowns\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " C +    A =  250     dinners    (1)   (counting dinners;  C = # of child;  A = # of adults)\r\n" );
document.write( "9C + 5.5A = 1935     dollars    (2)   ( counting dollars)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can solve it using the Substitution method. For it, express C = 250-A  from eq(1) and then substitute into eq(2).\r\n" );
document.write( "You will get\r\n" );
document.write( "\r\n" );
document.write( "9*(250-A) + 5.5A = 1935.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve for C.  \r\n" );
document.write( "When you find C, evaluate A = 250-C.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The rest is simple arithmetic, which I leave to you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Another approach is to start directly from one single equation \r\n" );
document.write( "\r\n" );
document.write( "9*(250-A) + 5.5A = 1935.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It also has simple interpretation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Again, simplify and solve for C.  \r\n" );
document.write( "When you find C, evaluate A = 250-C.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The rest is simple arithmetic, which I leave to you.\r\n" );
document.write( "

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

\n" );