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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 40200 ×
10
100
)(1
20
100
) ÷ (600 + 200) = ( x 40300 ×
15
100
)(1
20
100
) ÷ (600 + 100)
     Multiply both sides of the equation by:(600 + 200) ,  (600 + 100)
     ( x 40200 ×
10
100
)(1
20
100
)(600 + 100) = ( x 40300 ×
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 40300 ×
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
× 10040(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
× 10040(1
20
100
)(600 + 100)20 = 800 x x ×
20
100
× 600 x ×
20
100
× 20040(1
20
100
)(600 + 200)45
    The equation is reduced to :
     700 x x × 120 x × 2040(1
20
100
)(600 + 100)20(1
20
100
)(600 + 100) = 800 x x × 120 x × 4040(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 × 60040 × 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 × 60040 × 100 + 8(600 + 100)20(1
20
100
)(600 + 100) = 640 x 40 × 60040 × 200 + 8(600 + 200)45(1
20
100
)(600 + 200)
    The equation is reduced to :
     560 x 240004000 + 8(600 + 100)20(1
20
100
)(600 + 100) = 640 x 240008000 + 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 × 10020(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 × 10020(1
20
100
)(600 + 100) = 640 x 32000 + 8 × 600 + 8 × 20045(1
20
100
)(600 + 200)

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


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