SOLUTION: The problem states that 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

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Question 129649This question is from textbook Introductory Algebra
: The problem states that 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? This question is from textbook Introductory Algebra

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
80X+85Y=1225 OR 80X=1225-85Y OR X=(1225-85Y)/80
80(X+.5X)+85(Y-.2Y)=1540
80*1.5X+85*.8Y=1540
120X+68Y=1540
NOW REPLACE X BY (1225-85Y)/80
120(1225-85Y)/80+68Y=1540
1.5(1225-85Y)+68Y=1540
1837.5-127.5Y+68Y=1540
-59.5Y=1540-1837.5
-59.5Y=297.5
Y=-297.5/-59.5
Y=5 NUMBER OF THE ORIGINAL $85 HOURLY WORKERS.
X=(1225-85*5)/80
X=(1225-425)/80
X=800/80
X=10 NUMBER OF ORIGINAL $80 HOURLY WORKERS.
PROOF:
80*10+5*85=1225
800+425=1225
1225=1225