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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation X×（1-7%）×（1-5%）×（1-5%）×（1-4%） = 7.0 .
    Question type: Equation
    Solution:Original question:
      X (1 −
7
100
)(1 −
5
100
)(1 −
5
100
)(1 −
4
100
) = 7
    Remove the bracket on the left of the equation:
     Left side of the equation = X × 1(1 −
5
100
)(1 −
5
100
)(1 −
4
100
) − X ×
7
100
(1 −
5
100
)(1 −
5
100
)(1 −
4
100
)
                                             = X × 1 × 1(1 −
5
100
)(1 −
4
100
) − X × 1 ×
5
100
(1 −
5
100
)(1 −
4
100
) − X ×
7
100
                                             = X × 1(1 −
5
100
)(1 −
4
100
) − X ×
1
20
(1 −
5
100
)(1 −
4
100
) − X ×
7
100
(1 −
5
100
)(1 −
5
100
)
                                             = X × 1 × 1(1 −
4
100
) − X × 1 ×
5
100
(1 −
4
100
) − X ×
1
20
(1 −
5
100
)(1 −
4
100
)
                                             = X × 1(1 −
4
100
) − X ×
1
20
(1 −
4
100
) − X ×
1
20
(1 −
5
100
)(1 −
4
100
) − X ×
7
100
                                             = X × 1 × 1 − X × 1 ×
4
100
 − X ×
1
20
(1 −
4
100
) − X ×
1
20
(1 −
5
100
)
                                             = X × 1 − X ×
1
25
 − X ×
1
20
(1 −
4
100
) − X ×
1
20
(1 −
5
100
)(1 −
4
100
) − X
                                             =
24
25
 X − X ×
1
20
(1 −
4
100
) − X ×
1
20
(1 −
5
100
)(1 −
4
100
) − X ×
7
100
(1 −
5
100
)
                                             =
24
25
 X − X ×
1
20
 × 1 + X ×
1
20
 ×
4
100
 − X ×
1
20
(1 −
5
100
)(1 −
4
100
)
                                             =
24
25
 X − X ×
1
20
 + X ×
1
500
 − X ×
1
20
(1 −
5
100
)(1 −
4
100
) − X ×
7
100
                                             =
114
125
 X − X ×
1
20
(1 −
5
100
)(1 −
4
100
) − X ×
7
100
(1 −
5
100
)(1 −
5
100
)(1 −
4
100
)
                                             =
114
125
 X − X ×
1
20
 × 1(1 −
4
100
) + X ×
1
20
 ×
5
100
(1 −
4
100
) − X ×
7
100
                                             =
114
125
 X − X ×
1
20
(1 −
4
100
) + X ×
1
400
(1 −
4
100
) − X ×
7
100
(1 −
5
100
)(1 −
5
100
)
                                             =
114
125
 X − X ×
1
20
 × 1 + X ×
1
20
 ×
4
100
 + X ×
1
400
(1 −
4
100
) − X
                                             =
114
125
 X − X ×
1
20
 + X ×
1
500
 + X ×
1
400
(1 −
4
100
) − X ×
7
100
(1 −
5
100
)
                                             =
108
125
 X + X ×
1
400
(1 −
4
100
) − X ×
7
100
(1 −
5
100
)(1 −
5
100
)(1 −
4
100
)
                                             =
108
125
 X + X ×
1
400
 × 1 − X ×
1
400
 ×
4
100
 − X ×
7
100
(1 −
5
100
)(1 −
5
100
)
                                             =
108
125
 X + X ×
1
400
 − X ×
1
10000
 − X ×
7
100
(1 −
5
100
)(1 −
5
100
)(1 −
4
100
)
                                             =
1083
1250
 X − X ×
7
100
(1 −
5
100
)(1 −
5
100
)(1 −
4
100
)
                                             =
1083
1250
 X − X ×
7
100
 × 1(1 −
5
100
)(1 −
4
100
) + X ×
7
100
 ×
5
100
(1 −
5
100
)(1 −
4
100
)
                                             =
1083
1250
 X − X ×
7
100
(1 −
5
100
)(1 −
4
100
) + X ×
7
2000
(1 −
5
100
)(1 −
4
100
)
                                             =
1083
1250
 X − X ×
7
100
 × 1(1 −
4
100
) + X ×
7
100
 ×
5
100
(1 −
4
100
) + X ×
7
2000
                                             =
1083
1250
 X − X ×
7
100
(1 −
4
100
) + X ×
7
2000
(1 −
4
100
) + X ×
7
2000
(1 −
5
100
)(1 −
4
100
)
                                             =
1083
1250
 X − X ×
7
100
 × 1 + X ×
7
100
 ×
4
100
 + X ×
7
2000
(1 −
4
100
) + X
                                             =
1083
1250
 X − X ×
7
100
 + X ×
7
2500
 + X ×
7
2000
(1 −
4
100
) + X ×
7
2000
(1 −
5
100
)

    
        X≈8.687537 , keep 6 decimal places    
    There are 1 solution(s).

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