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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-40-200*10%)*(1-20%)/(600+200) = (x-40-300*15%)*(1-20%)/(600+100) .
    Question type: Equation
    Solution:Original question:
     ( x − 40 − 200 ×
10
100
)(1 −
20
100
) ÷ (600 + 200) = ( x − 40 − 300 ×
15
100
)(1 −
20
100
) ÷ (600 + 100)
     Multiply both sides of the equation by:(600 + 200) ,  (600 + 100)
     ( x − 40 − 200 ×
10
100
)(1 −
20
100
)(600 + 100) = ( x − 40 − 300 ×
15
100
)(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:：
      x (1 −
20
100
)(600 + 100) − 40(1 −
20
100
)(600 + 100) − 200 ×
10
100
(1 −
20
100
)(600 + 100) = ( x − 40 − 300 ×
15
100
)(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
      x (1 −
20
100
)(600 + 100) − 40(1 −
20
100
)(600 + 100) − 200 ×
10
100
(1 −
20
100
)(600 + 100) = x (1 −
20
100
)(600 + 200) − 40(1 −
20
100
)(600 + 200) − 300 ×
15
100
(1 −
20
100
)(600 + 200)
    The equation is reduced to :
      x (1 −
20
100
)(600 + 100) − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
)(600 + 100) = x (1 −
20
100
)(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:
      x × 1(600 + 100) − x ×
20
100
(600 + 100) − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
)(600 + 100) = x (1 −
20
100
)(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
      x × 1(600 + 100) − x ×
20
100
(600 + 100) − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
)(600 + 100) = x × 1(600 + 200) − x ×
20
100
(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:
      x × 1 × 600 + x × 1 × 100 − x ×
20
100
(600 + 100) − 40(1 −
20
100
)(600 + 100) = x × 1(600 + 200) − x ×
20
100
(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
      x × 1 × 600 + x × 1 × 100 − x ×
20
100
(600 + 100) − 40(1 −
20
100
)(600 + 100) = x × 1 × 600 + x × 1 × 200 − x ×
20
100
(600 + 200) − 40(1 −
20
100
)(600 + 200)
    The equation is reduced to :
      x × 600 + x × 100 − x ×
20
100
(600 + 100) − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
) = x × 600 + x × 200 − x ×
20
100
(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)
    The equation is reduced to :
     700 x − x ×
20
100
(600 + 100) − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
)(600 + 100) = 800 x − x ×
20
100
(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:
     700 x − x ×
20
100
 × 600 − x ×
20
100
 × 100 − 40(1 −
20
100
)(600 + 100) − 20 = 800 x − x ×
20
100
(600 + 200) − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
     700 x − x ×
20
100
 × 600 − x ×
20
100
 × 100 − 40(1 −
20
100
)(600 + 100) − 20 = 800 x − x ×
20
100
 × 600 − x ×
20
100
 × 200 − 40(1 −
20
100
)(600 + 200) − 45
    The equation is reduced to :
     700 x − x × 120 − x × 20 − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
)(600 + 100) = 800 x − x × 120 − x × 40 − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    The equation is reduced to :
     560 x − 40(1 −
20
100
)(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:
     560 x − 40 × 1(600 + 100) + 40 ×
20
100
(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 40(1 −
20
100
)(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
     560 x − 40 × 1(600 + 100) + 40 ×
20
100
(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 40 × 1(600 + 200) + 40 ×
20
100
(600 + 200) − 45(1 −
20
100
)(600 + 200)
    The equation is reduced to :
     560 x − 40(600 + 100) + 8(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 40(600 + 200) + 8(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:
     560 x − 40 × 600 − 40 × 100 + 8(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 40(600 + 200) + 8(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
     560 x − 40 × 600 − 40 × 100 + 8(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 40 × 600 − 40 × 200 + 8(600 + 200) − 45(1 −
20
100
)(600 + 200)
    The equation is reduced to :
     560 x − 24000 − 4000 + 8(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 24000 − 8000 + 8(600 + 200) − 45(1 −
20
100
)(600 + 200)
    The equation is reduced to :
     560 x − 28000 + 8(600 + 100) − 20(1 −
20
100
)(600 + 100) = 640 x − 32000 + 8(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the left of the equation:
     560 x − 28000 + 8 × 600 + 8 × 100 − 20(1 −
20
100
)(600 + 100) = 640 x − 32000 + 8(600 + 200) − 45(1 −
20
100
)(600 + 200)
    Remove a bracket on the right of the equation:：
     560 x − 28000 + 8 × 600 + 8 × 100 − 20(1 −
20
100
)(600 + 100) = 640 x − 32000 + 8 × 600 + 8 × 200 − 45(1 −
20
100
)(600 + 200)

    
        x=-39940    
    There are 1 solution(s).

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