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On line Solution of Monovariate Equation：
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    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation ((x-200)*(1-25%))/3300 = (x-200-150)*(1-25%)/3000 .
    Question type: Equation
    Solution:Original question:
     (( x − 200)(1 −
25
100
)) ÷ 3300 = ( x − 200 − 150)(1 −
25
100
) ÷ 3000
    Remove the bracket on the left of the equation:
     Left side of the equation = ( x − 200)(1 −
25
100
) ×
1
3300
                                             = x (1 −
25
100
) ×
1
3300
 − 200(1 −
25
100
) ×
1
3300
                                             = x (1 −
25
100
) ×
1
3300
 −
2
33
(1 −
25
100
)
                                             = x × 1 ×
1
3300
 − x ×
25
100
 ×
1
3300
 −
2
33
(1 −
25
100
)
                                             = x ×
1
3300
 − x ×
1
13200
 −
2
33
(1 −
25
100
)
                                             =
1
4400
 x −
2
33
(1 −
25
100
)
                                             =
1
4400
 x −
2
33
 × 1 +
2
33
 ×
25
100
                                             =
1
4400
 x −
2
33
 +
1
66
                                             =
1
4400
 x −
1
22
    The equation is transformed into :
     
1
4400
 x −
1
22
 = ( x − 200 − 150)(1 −
25
100
) ÷ 3000
    Remove the bracket on the right of the equation:
     Right side of the equation = x (1 −
25
100
) ×
1
3000
 − 200(1 −
25
100
) ×
1
3000
 − 150(1 −
25
100
) ×
1
3000
                                               = x (1 −
25
100
) ×
1
3000
 −
1
15
(1 −
25
100
) −
1
20
(1 −
25
100
)
                                               = x × 1 ×
1
3000
 − x ×
25
100
 ×
1
3000
 −
1
15
(1 −
25
100
) −
1
20
(1 −
25
100
)
                                               = x ×
1
3000
 − x ×
1
12000
 −
1
15
(1 −
25
100
) −
1
20
(1 −
25
100
)
                                               =
1
4000
 x −
1
15
(1 −
25
100
) −
1
20
(1 −
25
100
)
                                               =
1
4000
 x −
1
15
 × 1 +
1
15
 ×
25
100
 −
1
20
(1 −
25
100
)
                                               =
1
4000
 x −
1
15
 +
1
60
 −
1
20
(1 −
25
100
)
                                               =
1
4000
 x −
1
20
 −
1
20
(1 −
25
100
)
                                               =
1
4000
 x −
1
20
 −
1
20
 × 1 +
1
20
 ×
25
100
                                               =
1
4000
 x −
1
20
 −
1
20
 +
1
80
                                               =
1
4000
 x −
7
80
    The equation is transformed into :
     
1
4400
 x −
1
22
 =
1
4000
 x −
7
80

    Transposition :
     
1
4400
 x −
1
4000
 x = -
7
80
 +
1
22

    Combine the items on the left of the equation:
      -
1
44000
 x = -
7
80
 +
1
22

    Combine the items on the right of the equation:
      -
1
44000
 x = -
37
880

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
37
880
 =
1
44000
 x

    If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
     
1
44000
 x =
37
880

    The coefficient of the unknown number is reduced to 1 :
      x =
37
880
 ÷
1
44000
        =
37
880
 × 44000
        = 37 × 50

    We obtained :
      x = 1850
    This is the solution of the equation.



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