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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-1280)*(1-25%)/4000 = （X-1280-540）*（1-25%）/5250 .
    Question type: Equation
    Solution:Original question:
     ( X − 1280)(1 −
25
100
) ÷ 4000 = ( X − 1280 − 540)(1 −
25
100
) ÷ 5250
    Remove the bracket on the left of the equation:
     Left side of the equation = X (1 −
25
100
) ×
1
4000
 − 1280(1 −
25
100
) ×
1
4000
                                             = X (1 −
25
100
) ×
1
4000
 −
8
25
(1 −
25
100
)
                                             = X × 1 ×
1
4000
 − X ×
25
100
 ×
1
4000
 −
8
25
(1 −
25
100
)
                                             = X ×
1
4000
 − X ×
1
16000
 −
8
25
(1 −
25
100
)
                                             =
3
16000
 X −
8
25
(1 −
25
100
)
                                             =
3
16000
 X −
8
25
 × 1 +
8
25
 ×
25
100
                                             =
3
16000
 X −
8
25
 +
2
25
                                             =
3
16000
 X −
6
25
    The equation is transformed into :
     
3
16000
 X −
6
25
 = ( X − 1280 − 540)(1 −
25
100
) ÷ 5250
    Remove the bracket on the right of the equation:
     Right side of the equation = X (1 −
25
100
) ×
1
5250
 − 1280(1 −
25
100
) ×
1
5250
 − 540(1 −
25
100
) ×
1
5250
                                               = X (1 −
25
100
) ×
1
5250
 −
128
525
(1 −
25
100
) −
18
175
(1 −
25
100
)
                                               = X × 1 ×
1
5250
 − X ×
25
100
 ×
1
5250
 −
128
525
(1 −
25
100
) −
18
175
(1 −
25
100
)
                                               = X ×
1
5250
 − X ×
1
21000
 −
128
525
(1 −
25
100
) −
18
175
(1 −
25
100
)
                                               =
1
7000
 X −
128
525
(1 −
25
100
) −
18
175
(1 −
25
100
)
                                               =
1
7000
 X −
128
525
 × 1 +
128
525
 ×
25
100
 −
18
175
(1 −
25
100
)
                                               =
1
7000
 X −
128
525
 +
32
525
 −
18
175
(1 −
25
100
)
                                               =
1
7000
 X −
32
175
 −
18
175
(1 −
25
100
)
                                               =
1
7000
 X −
32
175
 −
18
175
 × 1 +
18
175
 ×
25
100
                                               =
1
7000
 X −
32
175
 −
18
175
 +
9
350
                                               =
1
7000
 X −
13
50
    The equation is transformed into :
     
3
16000
 X −
6
25
 =
1
7000
 X −
13
50

    Transposition :
     
3
16000
 X −
1
7000
 X = -
13
50
 +
6
25

    Combine the items on the left of the equation:
     
1
22400
 X = -
13
50
 +
6
25

    Combine the items on the right of the equation:
     
1
22400
 X = -
1
50

    The coefficient of the unknown number is reduced to 1 :
      X = -
1
50
 ÷
1
22400
        = -
1
50
 × 22400
        = - 1 × 448

    We obtained :
      X = - 448
    This is the solution of the equation.



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