An employer has a daily payroll of 1225.00 when employing some workers at 80.00 per day and others at 85.00 per day. When the number of 80.00 workers increases by 50% and the number of 85.00 workers is decreased by 1/5, the new daily payroll is 1540.00. How many were originally employed at each rate?

I got the two equations:

1225=80x+85y and 1540=120x+68y

Then used the substitution method and ended up with

x=20.37 and y=-4.76

So if did this correct than x and y should equal the number of workers originally employed at each rate.

Did I do this right?

well i gues you did it rigth but i am not sure.

Something must be wrong because both x and y should be positive integers.

Let's quickly get rid of x.
3675 = 240x + 255y
3080 = 240x + 136y
------------------
595 = 119 y
y = 5
1225 = 80x + 425
80x = 800
x = 10

thanks for the help, I didn't realize you could line up the equations and solve that way by multiplying them to get a matching integer and then subtracting.

THANKS, for teaching so well!

Based on the equations you provided, we can solve for the number of workers originally employed at each rate. Let's go through the steps:

Step 1: Set up the equations:
- 1225 = 80x + 85y
- 1540 = 120x + 68y

Step 2: Solve the equations simultaneously using the substitution method:
From the first equation, isolate x in terms of y:
80x = 1225 - 85y
x = (1225 - 85y)/80

Substitute this value in the second equation:
1540 = 120((1225 - 85y)/80) + 68y

Step 3: Simplify and solve for y:
1540 = (14625 - 1020y)/80 + 68y
1540 = 182.81 - 12.75y + 68y
1540 - 182.81 = 55.25y
1357.19 = 55.25y
y = 1357.19 / 55.25
y ≈ 24.55

Step 4: Substitute the value of y back into the first equation to solve for x:
x = (1225 - 85(24.55))/80
x ≈ 13.77

Therefore, there were approximately 13.77 workers originally employed at a rate of $80.00 per day and 24.55 workers originally employed at a rate of $85.00 per day. Note that the number of workers cannot be negative, so we can consider the value of y as 25 since fractions of a worker make no sense in this context.