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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-20-36)*(1-25%)}/80 = {(x-20)*(1-25%)}/100 .
    Question type: Equation
    Solution:Original question:
     (( x − 20 − 36)(1 −
25
100
)) ÷ 80 = (( x − 20)(1 −
25
100
)) ÷ 100
    Remove the bracket on the left of the equation:
     Left side of the equation = ( x − 20 − 36)(1 −
25
100
) ×
1
80
                                             = x (1 −
25
100
) ×
1
80
 − 20(1 −
25
100
) ×
1
80
 − 36(1 −
25
100
) ×
1
80
                                             = x (1 −
25
100
) ×
1
80
 −
1
4
(1 −
25
100
) −
9
20
(1 −
25
100
)
                                             = x × 1 ×
1
80
 − x ×
25
100
 ×
1
80
 −
1
4
(1 −
25
100
) −
9
20
(1 −
25
100
)
                                             = x ×
1
80
 − x ×
1
320
 −
1
4
(1 −
25
100
) −
9
20
(1 −
25
100
)
                                             =
3
320
 x −
1
4
(1 −
25
100
) −
9
20
(1 −
25
100
)
                                             =
3
320
 x −
1
4
 × 1 +
1
4
 ×
25
100
 −
9
20
(1 −
25
100
)
                                             =
3
320
 x −
1
4
 +
1
16
 −
9
20
(1 −
25
100
)
                                             =
3
320
 x −
3
16
 −
9
20
(1 −
25
100
)
                                             =
3
320
 x −
3
16
 −
9
20
 × 1 +
9
20
 ×
25
100
                                             =
3
320
 x −
3
16
 −
9
20
 +
9
80
                                             =
3
320
 x −
21
40
    The equation is transformed into :
     
3
320
 x −
21
40
 = (( x − 20)(1 −
25
100
)) ÷ 100
    Remove the bracket on the right of the equation:
     Right side of the equation = ( x − 20)(1 −
25
100
) ×
1
100
                                               = x (1 −
25
100
) ×
1
100
 − 20(1 −
25
100
) ×
1
100
                                               = x (1 −
25
100
) ×
1
100
 −
1
5
(1 −
25
100
)
                                               = x × 1 ×
1
100
 − x ×
25
100
 ×
1
100
 −
1
5
(1 −
25
100
)
                                               = x ×
1
100
 − x ×
1
400
 −
1
5
(1 −
25
100
)
                                               =
3
400
 x −
1
5
(1 −
25
100
)
                                               =
3
400
 x −
1
5
 × 1 +
1
5
 ×
25
100
                                               =
3
400
 x −
1
5
 +
1
20
                                               =
3
400
 x −
3
20
    The equation is transformed into :
     
3
320
 x −
21
40
 =
3
400
 x −
3
20

    Transposition :
     
3
320
 x −
3
400
 x = -
3
20
 +
21
40

    Combine the items on the left of the equation:
     
3
1600
 x = -
3
20
 +
21
40

    Combine the items on the right of the equation:
     
3
1600
 x =
3
8

    The coefficient of the unknown number is reduced to 1 :
      x =
3
8
 ÷
3
1600
        =
3
8
 ×
1600
3
        = 1 × 200

    We obtained :
      x = 200
    This is the solution of the equation.



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