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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    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—30）*（1—30%）/400 = （x—40）*（1—20%）/200 .
    Question type: Equation
    Solution:Original question:
     ( x − 30)(1 −
30
100
) ÷ 400 = ( x − 40)(1 −
20
100
) ÷ 200
    Remove the bracket on the left of the equation:
     Left side of the equation = x (1 −
30
100
) ×
1
400
 − 30(1 −
30
100
) ×
1
400
                                             = x (1 −
30
100
) ×
1
400
 −
3
40
(1 −
30
100
)
                                             = x × 1 ×
1
400
 − x ×
30
100
 ×
1
400
 −
3
40
(1 −
30
100
)
                                             = x ×
1
400
 − x ×
3
4000
 −
3
40
(1 −
30
100
)
                                             =
7
4000
 x −
3
40
(1 −
30
100
)
                                             =
7
4000
 x −
3
40
 × 1 +
3
40
 ×
30
100
                                             =
7
4000
 x −
3
40
 +
9
400
                                             =
7
4000
 x −
21
400
    The equation is transformed into :
     
7
4000
 x −
21
400
 = ( x − 40)(1 −
20
100
) ÷ 200
    Remove the bracket on the right of the equation:
     Right side of the equation = x (1 −
20
100
) ×
1
200
 − 40(1 −
20
100
) ×
1
200
                                               = x (1 −
20
100
) ×
1
200
 −
1
5
(1 −
20
100
)
                                               = x × 1 ×
1
200
 − x ×
20
100
 ×
1
200
 −
1
5
(1 −
20
100
)
                                               = x ×
1
200
 − x ×
1
1000
 −
1
5
(1 −
20
100
)
                                               =
1
250
 x −
1
5
(1 −
20
100
)
                                               =
1
250
 x −
1
5
 × 1 +
1
5
 ×
20
100
                                               =
1
250
 x −
1
5
 +
1
25
                                               =
1
250
 x −
4
25
    The equation is transformed into :
     
7
4000
 x −
21
400
 =
1
250
 x −
4
25

    Transposition :
     
7
4000
 x −
1
250
 x = -
4
25
 +
21
400

    Combine the items on the left of the equation:
      -
9
4000
 x = -
4
25
 +
21
400

    Combine the items on the right of the equation:
      -
9
4000
 x = -
43
400

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
43
400
 =
9
4000
 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 :
     
9
4000
 x =
43
400

    The coefficient of the unknown number is reduced to 1 :
      x =
43
400
 ÷
9
4000
        =
43
400
 ×
4000
9
        = 43 ×
10
9

    We obtained :
      x =
430
9
    This is the solution of the equation.

    Convert the result to decimal form :
      x = 47.777778



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