# Math Question: Challenge. The Question is Big, please look for it in the description/detail?

A company figured that if it had 50 more employees and paid each one \$2 per day less, the payroll would increase by \$620 per day. If it had 50 less employees and paid \$4 per day more , the payrool would decrease \$640 per day. How many employees does the company now have

• P = np

P + 620 = np + 620 = (n+50)(p-2) = np -2n + 50p – 100

P – 640 = np – 640 = (n-50)(p+4) = np + 4n – 50p – 200

620 = 50p – 2n – 100

640 = 50p – 4n + 200

20 = -2n + 300

2n = 280

n = 140

The company currently has 140 employees and pays them an average of 20 per day.

• A company figured that if it had 50 more employees and paid each one \$2 per day less, the payroll would increase by \$620 per day.

(e+50)*\$2=\$p+\$620

If it had 50 less employees and paid \$4 per day more , the payroll would decrease \$640 per day.

(e-50)*\$4=\$p-\$640

you might need to solve for three variables

employees=e

rate of pay=r

payroll=p

(e+50)*(r-\$2)=(\$p+\$620)

see what I mean?

and

(e-50)*(r+\$4)=(\$p-\$640)

beyond that……

matrices hate me

• Let x = original number of employed @ \$y per day

Original payroll = xy

(x+50)(y-2) = xy +620

xy -2x +50y -100 = xy +620

-2x +50 y = 720 (1)

(x-50)(y+4) = xy -640

xy +4x -50y -200 = xy -640

`` 4x -50y = -440   (2)``

(1) +(2) gives 2x = 280

``                  x = 140``

The company has 140 employees now.

• Let Y represent the number of employees now.

Let \$X represent each employees’ daily wage now. {{{ they are getting slave labour }}}

Therefore the daily payroll now is \$(XY). {{{ multiply them }}}

The information can be put into two equations:

First >>>

XY + 620 = ( X – 2 )( Y + 50 )

XY + 620 = XY + 50X -2Y – 100

620 = 50X – 2Y -100

720 = 50X – 2Y

360 = 25X – Y

Y = 25X – 360

Second>>>

XY – 640 = ( X + 4 )( Y – 50 )

XY – 640 = XY – 50X + 4Y – 200

-640 = -50X + 4Y -200

-440 = -50X + 4Y

4Y – 50X = -440

4Y = 50X – 440

Y = 12.5X – 110

Combine the First and the Second

25X – 360 = 12.5X – 110

12.5X = 250

X = 20

Now use the simplifed First equation (or the Second)

Y = 25X – 360

Y = 25(20) – 360

Y = 500 – 360

Y = 140

The company has 140 employees now. {{{ they pay them \$20 each per day }}}

• x = current employees

y = salary of current employee(per day)

(x + 50)(y – 2) = xy + 620

(x – 50)(y + 4) = xy – 640

-2x + 50y = 720

4x – 50y = -440