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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation (X-200)*(1-25%)/3000 = (X-200-150)*(1-25%)/3300 .
    Question type: Equation
    Solution:Original question:
     ( X 200)(1
25
100
) ÷ 3000 = ( X 200150)(1
25
100
) ÷ 3300
    Remove the bracket on the left of the equation:
     Left side of the equation = X (1
25
100
) ×
1
3000
200(1
25
100
) ×
1
3000
                                             = X (1
25
100
) ×
1
3000
1
15
(1
25
100
)
                                             = X × 1 ×
1
3000
X ×
25
100
×
1
3000
1
15
(1
25
100
)
                                             = X ×
1
3000
X ×
1
12000
1
15
(1
25
100
)
                                             =
1
4000
X
1
15
(1
25
100
)
                                             =
1
4000
X
1
15
× 1 +
1
15
×
25
100
                                             =
1
4000
X
1
15
+
1
60
                                             =
1
4000
X
1
20
    The equation is transformed into :
     
1
4000
X
1
20
= ( X 200150)(1
25
100
) ÷ 3300
    Remove the bracket on the right of the equation:
     Right side of the equation = X (1
25
100
) ×
1
3300
200(1
25
100
) ×
1
3300
150(1
25
100
) ×
1
3300
                                               = X (1
25
100
) ×
1
3300
2
33
(1
25
100
)
1
22
(1
25
100
)
                                               = X × 1 ×
1
3300
X ×
25
100
×
1
3300
2
33
(1
25
100
)
1
22
(1
25
100
)
                                               = X ×
1
3300
X ×
1
13200
2
33
(1
25
100
)
1
22
(1
25
100
)
                                               =
1
4400
X
2
33
(1
25
100
)
1
22
(1
25
100
)
                                               =
1
4400
X
2
33
× 1 +
2
33
×
25
100
1
22
(1
25
100
)
                                               =
1
4400
X
2
33
+
1
66
1
22
(1
25
100
)
                                               =
1
4400
X
1
22
1
22
(1
25
100
)
                                               =
1
4400
X
1
22
1
22
× 1 +
1
22
×
25
100
                                               =
1
4400
X
1
22
1
22
+
1
88
                                               =
1
4400
X
7
88
    The equation is transformed into :
     
1
4000
X
1
20
=
1
4400
X
7
88

    Transposition :
     
1
4000
X
1
4400
X = -
7
88
+
1
20

    Combine the items on the left of the equation:
     
1
44000
X = -
7
88
+
1
20

    Combine the items on the right of the equation:
     
1
44000
X = -
13
440

    The coefficient of the unknown number is reduced to 1 :
      X = -
13
440
÷
1
44000
        = -
13
440
× 44000
        = - 13 × 100

    We obtained :
      X = - 1300
    This is the solution of the equation.



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