document.write( "Question 111615: 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? \n" ); document.write( "
Algebra.Com's Answer #81652 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
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?
\n" ); document.write( ":
\n" ); document.write( "Let x = original number of $80 workers (when payroll was $1225)
\n" ); document.write( "and
\n" ); document.write( "Let y = original number of $85 workers
\n" ); document.write( ":
\n" ); document.write( "Then:
\n" ); document.write( "1.5x = number of $80 workers when payroll is $1540 (a 50% increase)
\n" ); document.write( "and
\n" ); document.write( ".8x = number of $85 workers (= a 20% decrease which is 1/5)
\n" ); document.write( ":
\n" ); document.write( "An equation for each scenario
\n" ); document.write( "80x + 85y = 1225
\n" ); document.write( "and
\n" ); document.write( "1.5(80x) + .8(85y) = 1540
\n" ); document.write( "which is:
\n" ); document.write( "120x + 68y = 1540
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 1.5 and subtract the 2nd equation:
\n" ); document.write( "120x + 127.5y = 1837.5
\n" ); document.write( "120x + 68y = 1540
\n" ); document.write( "---------------------subtracting eliminates x, find y
\n" ); document.write( "0x + 59.5y = 297.5
\n" ); document.write( "y = 297.5/59.5
\n" ); document.write( "y = 5 ea $85 workers originally
\n" ); document.write( ":
\n" ); document.write( "Find x using the 1st equation:
\n" ); document.write( "80x + 85(5) = 1225
\n" ); document.write( "80x + 425 = 1225
\n" ); document.write( "80x = 1225 - 425
\n" ); document.write( "80x = 800
\n" ); document.write( "x = 10 ea $80 workers originally
\n" ); document.write( ":
\n" ); document.write( "Check solution using the 2nd scenario; 15 $80 workers and 4 $85 workers
\n" ); document.write( "80(15) + 4(85) = 1540:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "
\n" );