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?

Question

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?

Answer 1

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?

Answer 2

still stuck

Answer 3

To solve this problem, let's assume the original number of workers who earned $80.00 per day is x, and the original number of workers who earned $85.00 per day is y.

We know the original daily payroll is $1225.00, so we can set up the following equation:

80x + 85y = 1225.00 ---(Equation 1)

Afterward, we can set up a second equation using the information given in the problem. According to the problem, the number of workers earning $80.00 per day increases by 50% (which can be expressed as 1.5x), and the number of workers earning $85.00 per day decreases by 1/5 (which can be expressed as 0.8y). The resulting daily payroll is $1540.00, giving us the second equation:

80*(1.5x) + 85*(0.8y) = 1540.00 ---(Equation 2)

Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system of equations using the method of substitution or elimination.

Let's solve it using the method of substitution. Rearrange Equation 2 to solve for x:

120x + 68y = 1540.00 ---(Equation 3)

Now we can substitute Equation 3 into Equation 1:

120x + 68y = 1540.00 ---(Equation 3)
80x + 85y = 1225.00 ---(Equation 1)

Multiply Equation 1 by 1.5 to make the coefficients of x in both equations the same:

120x + 127.5y = 1837.50 ---(Equation 4)

We now have a system of two equations:

120x + 68y = 1540.00 ---(Equation 3)
120x + 127.5y = 1837.50 ---(Equation 4)

Subtract Equation 3 from Equation 4 to eliminate x:

(120x + 127.5y) - (120x + 68y) = 1837.50 - 1540.00
59.5y = 297.50

Divide both sides of the equation by 59.5 to solve for y:

y = 297.50 / 59.5
y = 5

Now substitute the value of y back into Equation 3 to find x:

120x + 68(5) = 1540.00
120x + 340 = 1540.00
120x = 1200.00
x = 10

Therefore, the original number of workers earning $80.00 per day was 10, and the original number of workers earning $85.00 per day was 5.