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    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation （x-500）×（1-25%）÷3000 = （x-1000×10%）×（1-25%）÷（3000+2000） .
    Question type: Equation
    Solution:Original question:
     ( x − 500)(1 −
25
100
) ÷ 3000 = ( x − 1000 ×
10
100
)(1 −
25
100
) ÷ (3000 + 2000)
     Multiply both sides of the equation by:(3000 + 2000)
     ( x − 500)(1 −
25
100
) ÷ 3000 × (3000 + 2000) = ( x − 1000 ×
10
100
)(1 −
25
100
)
    Remove a bracket on the left of the equation:：
      x (1 −
25
100
) ÷ 3000 × (3000 + 2000) − 500(1 −
25
100
) ÷ 3000 × (3000 + 2000) = ( x − 1000 ×
10
100
)(1 −
25
100
)
    Remove a bracket on the right of the equation:：
      x (1 −
25
100
) ÷ 3000 × (3000 + 2000) − 500(1 −
25
100
) ÷ 3000 × (3000 + 2000) = x (1 −
25
100
) − 1000 ×
10
100
(1 −
25
100
)
    The equation is reduced to :
      x (1 −
25
100
) ×
1
3000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) = x (1 −
25
100
) − 100(1 −
25
100
)
    Remove a bracket on the left of the equation:
      x × 1 ×
1
3000
(3000 + 2000) − x ×
25
100
 ×
1
3000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) = x (1 −
25
100
) − 100(1 −
25
100
)
    Remove a bracket on the right of the equation:：
      x × 1 ×
1
3000
(3000 + 2000) − x ×
25
100
 ×
1
3000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) = x × 1 − x ×
25
100
 − 100(1 −
25
100
)
    The equation is reduced to :
      x ×
1
3000
(3000 + 2000) − x ×
1
12000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) = x × 1 − x ×
25
100
 − 100(1 −
25
100
)
    The equation is reduced to :
      x ×
1
3000
(3000 + 2000) − x ×
1
12000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 100(1 −
25
100
)
    Remove a bracket on the left of the equation:
      x ×
1
3000
 × 3000 + x ×
1
3000
 × 2000 − x ×
1
12000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 100(1 −
25
100
)
    Remove a bracket on the right of the equation:：
      x ×
1
3000
 × 3000 + x ×
1
3000
 × 2000 − x ×
1
12000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 100 × 1 + 100 ×
25
100
    The equation is reduced to :
      x × 1 + x ×
2
3
 − x ×
1
12000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 100 + 25
    The equation is reduced to :
     
5
3
 x − x ×
1
12000
(3000 + 2000) −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 75
    Remove a bracket on the left of the equation:
     
5
3
 x − x ×
1
12000
 × 3000 − x ×
1
12000
 × 2000 −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 75
    The equation is reduced to :
     
5
3
 x − x ×
1
4
 − x ×
1
6
 −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 75
    The equation is reduced to :
     
5
4
 x −
1
6
(1 −
25
100
)(3000 + 2000) =
3
4
 x − 75
    Remove a bracket on the left of the equation:
     
5
4
 x −
1
6
 × 1(3000 + 2000) +
1
6
 ×
25
100
(3000 + 2000) =
3
4
 x − 75
    The equation is reduced to :
     
5
4
 x −
1
6
(3000 + 2000) +
1
24
(3000 + 2000) =
3
4
 x − 75
    Remove a bracket on the left of the equation:
     
5
4
 x −
1
6
 × 3000 −
1
6
 × 2000 +
1
24
(3000 + 2000) =
3
4
 x − 75
    The equation is reduced to :
     
5
4
 x − 500 −
1000
3
 +
1
24
(3000 + 2000) =
3
4
 x − 75
    The equation is reduced to :
     
5
4
 x −
2500
3
 +
1
24
(3000 + 2000) =
3
4
 x − 75
    Remove a bracket on the left of the equation:
     
5
4
 x −
2500
3
 +
1
24
 × 3000 +
1
24
 × 2000 =
3
4
 x − 75
    The equation is reduced to :
     
5
4
 x −
2500
3
 + 125 +
250
3
 =
3
4
 x − 75
    The equation is reduced to :
     
5
4
 x − 625 =
3
4
 x − 75

    Transposition :
     
5
4
 x −
3
4
 x = - 75 + 625

    Combine the items on the left of the equation:
     
1
2
 x = - 75 + 625

    Combine the items on the right of the equation:
     
1
2
 x = 550

    The coefficient of the unknown number is reduced to 1 :
      x = 550 ÷
1
2
        = 550 × 2

    We obtained :
      x = 1100
    This is the solution of the equation.



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