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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-400*5%-600*6%)*(1-25%)/800 = (x-400*5%)*（1-25%）/820 .
    Question type: Equation
    Solution:Original question:
     ( x − 400 ×
5
100
 − 600 ×
6
100
)(1 −
25
100
) ÷ 800 = ( x − 400 ×
5
100
)(1 −
25
100
) ÷ 820
    Remove the bracket on the left of the equation:
     Left side of the equation = x (1 −
25
100
) ×
1
800
 − 400 ×
5
100
(1 −
25
100
) ×
1
800
 − 600 ×
6
100
(1 −
25
100
) ×
1
800
                                             = x (1 −
25
100
) ×
1
800
 −
1
40
(1 −
25
100
) −
9
200
(1 −
25
100
)
                                             = x × 1 ×
1
800
 − x ×
25
100
 ×
1
800
 −
1
40
(1 −
25
100
) −
9
200
(1 −
25
100
)
                                             = x ×
1
800
 − x ×
1
3200
 −
1
40
(1 −
25
100
) −
9
200
(1 −
25
100
)
                                             =
3
3200
 x −
1
40
(1 −
25
100
) −
9
200
(1 −
25
100
)
                                             =
3
3200
 x −
1
40
 × 1 +
1
40
 ×
25
100
 −
9
200
(1 −
25
100
)
                                             =
3
3200
 x −
1
40
 +
1
160
 −
9
200
(1 −
25
100
)
                                             =
3
3200
 x −
3
160
 −
9
200
(1 −
25
100
)
                                             =
3
3200
 x −
3
160
 −
9
200
 × 1 +
9
200
 ×
25
100
                                             =
3
3200
 x −
3
160
 −
9
200
 +
9
800
                                             =
3
3200
 x −
21
400
    The equation is transformed into :
     
3
3200
 x −
21
400
 = ( x − 400 ×
5
100
)(1 −
25
100
) ÷ 820
    Remove the bracket on the right of the equation:
     Right side of the equation = x (1 −
25
100
) ×
1
820
 − 400 ×
5
100
(1 −
25
100
) ×
1
820
                                               = x (1 −
25
100
) ×
1
820
 −
1
41
(1 −
25
100
)
                                               = x × 1 ×
1
820
 − x ×
25
100
 ×
1
820
 −
1
41
(1 −
25
100
)
                                               = x ×
1
820
 − x ×
1
3280
 −
1
41
(1 −
25
100
)
                                               =
3
3280
 x −
1
41
(1 −
25
100
)
                                               =
3
3280
 x −
1
41
 × 1 +
1
41
 ×
25
100
                                               =
3
3280
 x −
1
41
 +
1
164
                                               =
3
3280
 x −
3
164
    The equation is transformed into :
     
3
3200
 x −
21
400
 =
3
3280
 x −
3
164

    Transposition :
     
3
3200
 x −
3
3280
 x = -
3
164
 +
21
400

    Combine the items on the left of the equation:
     
3
131200
 x = -
3
164
 +
21
400

    Combine the items on the right of the equation:
     
3
131200
 x =
561
16400

    The coefficient of the unknown number is reduced to 1 :
      x =
561
16400
 ÷
3
131200
        =
561
16400
 ×
131200
3
        = 187 × 8

    We obtained :
      x = 1496
    This is the solution of the equation.



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