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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
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?
:
Let x = original number of $80 workers (when payroll was $1225)
and
Let y = original number of $85 workers
:
Then:
1.5x = number of $80 workers when payroll is $1540 (a 50% increase)
and
.8x = number of $85 workers (= a 20% decrease which is 1/5)
:
An equation for each scenario
80x + 85y = 1225
and
1.5(80x) + .8(85y) = 1540
which is:
120x + 68y = 1540
:
Multiply the 1st equation by 1.5 and subtract the 2nd equation:
120x + 127.5y = 1837.5
120x + 68y = 1540
---------------------subtracting eliminates x, find y
0x + 59.5y = 297.5
y = 297.5/59.5
y = 5 ea $85 workers originally
:
Find x using the 1st equation:
80x + 85(5) = 1225
80x + 425 = 1225
80x = 1225 - 425
80x = 800
x = 10 ea $80 workers originally
:
Check solution using the 2nd scenario; 15 $80 workers and 4 $85 workers
80(15) + 4(85) = 1540:
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