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

5 Answers

  • 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

    Adding both eqns:

    2x = 280

    x = 140 current employees

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