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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 10% = 9%×(1/55%)×X/(1-9%×(1/55%)×X) .
    Question type: Equation
    Solution:Original question:
     
10
100
=
9
100
(1 ÷
55
100
) X ÷ (1
9
100
(1 ÷
55
100
) X )
     Multiply both sides of the equation by:(1
9
100
(1 ÷
55
100
) X )
     
10
100
(1
9
100
(1 ÷
55
100
) X ) =
9
100
(1 ÷
55
100
) X
    Remove a bracket on the left of the equation::
     
10
100
× 1
10
100
×
9
100
(1 ÷
55
100
) X =
9
100
(1 ÷
55
100
) X
    Remove a bracket on the right of the equation::
     
10
100
× 1
10
100
×
9
100
(1 ÷
55
100
) X =
9
100
× 1 ÷
55
100
× X
    The equation is reduced to :
     
1
10
9
1000
(1 ÷
55
100
) X =
9
55
X
    Remove a bracket on the left of the equation:
     
1
10
9
1000
× 1 ÷
55
100
× X =
9
55
X
    The equation is reduced to :
     
1
10
9
550
X =
9
55
X

    Transposition :
      -
9
550
X
9
55
X = -
1
10

    Combine the items on the left of the equation:
      -
9
50
X = -
1
10

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     
1
10
=
9
50
X

    If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
     
9
50
X =
1
10

    The coefficient of the unknown number is reduced to 1 :
      X =
1
10
÷
9
50
        =
1
10
×
50
9
        = 1 ×
5
9

    We obtained :
      X =
5
9
    This is the solution of the equation.

    Convert the result to decimal form :
      X = 0.555556



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