document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154053>Question 154053</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Employer Payroll.  An employer has a daily payroll of $1225 when employing some workers at $80 per day and others at $85 per day.  When the number of $80 workers is increased by 50% and the number of $85 workers is decreased by 1/5, the new daily payroll is $1540.  How many were originally employed at each rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113454 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=113454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An employer has a daily payroll of $1225 when employing some workers at $80 per day and others at $85 per day. When the number of $80 workers is increased by 50% and the number of $85 workers is decreased by 1/5, the new daily payroll is $1540. How many were originally employed at each rate?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = no. of $80 workers (originally)<BR>\n" );
document.write( "Let y = no. of $85 workers<BR>\n" );
document.write( ":<BR>\n" );
document.write( "$1225 payroll equation<BR>\n" );
document.write( "80x + 85y = 1225<BR>\n" );
document.write( ":<BR>\n" );
document.write( "$1540 payroll equation; (50% increase = 1.5; and 1/5 decrease = .8<BR>\n" );
document.write( "80(1.5x) + 85(.8y) = 1540<BR>\n" );
document.write( "120x + 68y = 1540<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 1.5 and subtract the above equation:<BR>\n" );
document.write( "120x + 127.5y = 1837.5<BR>\n" );
document.write( "120x +  68.0y = 1540<BR>\n" );
document.write( "------------------------subtraction eliminates x, find y:<BR>\n" );
document.write( "0x + 59.5y = 297.5<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=297.5%2F59.5 ALIGN=MIDDLE  ALT=\"297.5%2F59.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 5 ea $85 workers originally<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find x using the 1st equation:<BR>\n" );
document.write( "80x + 85(5) = 1225<BR>\n" );
document.write( "80x + 425 = 1225<BR>\n" );
document.write( "80x = 1225 - 425<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800%2F80 ALIGN=MIDDLE  ALT=\"800%2F80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 10 ea $80 workers originally<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution in equation: 120x + 68y = 1540<BR>\n" );
document.write( "120(10) + 68(5) = 1540, confirms our solutions </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );