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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 117-117/（1+17%）*17%*（1+7%+3%+2%） = W-W/（1+3%）*3%*（1+7%+3%+2%） .
    Question type: Equation
    Solution:Original question:
     117 − 117 ÷ (1 +
17
100
) ×
17
100
(1 +
7
100
 +
3
100
 +
2
100
) = W − W ÷ (1 +
3
100
) ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)
     Multiply both sides of the equation by:(1 +
17
100
) ,  (1 +
3
100
)
     117(1 +
17
100
)(1 +
3
100
) − 117 ×
17
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W (1 +
17
100
)(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the left of the equation:：
     117 × 1(1 +
3
100
) + 117 ×
17
100
(1 +
3
100
) − 117 ×
17
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W (1 +
17
100
)(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the right of the equation:：
     117 × 1(1 +
3
100
) + 117 ×
17
100
(1 +
3
100
) − 117 ×
17
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W × 1(1 +
3
100
) + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    The equation is reduced to :
     117(1 +
3
100
) +
1989
100
(1 +
3
100
) −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W × 1(1 +
3
100
) + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the left of the equation:
     117 × 1 + 117 ×
3
100
 +
1989
100
(1 +
3
100
) −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W × 1(1 +
3
100
) + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the right of the equation:：
     117 × 1 + 117 ×
3
100
 +
1989
100
(1 +
3
100
) −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W × 1 × 1 + W × 1 ×
3
100
 + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)
    The equation is reduced to :
     117 +
351
100
 +
1989
100
(1 +
3
100
) −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) = W × 1 + W ×
3
100
 + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    The equation is reduced to :
     
12051
100
 +
1989
100
(1 +
3
100
) −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) =
103
100
 W + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the left of the equation:
     
12051
100
 +
1989
100
 × 1 +
1989
100
 ×
3
100
 −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) =
103
100
 W + W ×
17
100
(1 +
3
100
) − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the right of the equation:：
     
12051
100
 +
1989
100
 × 1 +
1989
100
 ×
3
100
 −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) =
103
100
 W + W ×
17
100
 × 1 + W ×
17
100
 ×
3
100
 − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    The equation is reduced to :
     
12051
100
 +
1989
100
 +
5967
10000
 −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) =
103
100
 W + W ×
17
100
 + W ×
51
10000
 − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    The equation is reduced to :
     
1409967
10000
 −
1989
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
3
100
) =
12051
10000
 W − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the left of the equation:
     
1409967
10000
 −
1989
100
 × 1(1 +
3
100
) −
1989
100
 ×
7
100
(1 +
3
100
) −
1989
100
 ×
3
100
(1 +
3
100
) −
1989
100
 ×
2
100
 =
12051
10000
 W − W ×
3
100
(1 +
7
100
 +
3
100
 +
2
100
)(1 +
17
100
)
    Remove a bracket on the right of the equation:：
     
1409967
10000
 −
1989
100
 × 1(1 +
3
100
) −
1989
100
 ×
7
100
(1 +
3
100
) −
1989
100
 ×
3
100
(1 +
3
100
) −
1989
100
 ×
2
100
 =
12051
10000
 W − W ×
3
100
 × 1(1 +
17
100
) − W ×
3
100
 ×
7
100
(1 +
17
100
) − W ×
3
100
    The equation is reduced to :
     
1409967
10000
 −
1989
100
(1 +
3
100
) −
13923
10000
(1 +
3
100
) −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
12051
10000
 W − W ×
3
100
(1 +
17
100
) − W ×
21
10000
(1 +
17
100
) − W ×
9
10000
(1 +
17
100
) − W
    Remove a bracket on the left of the equation:
     
1409967
10000
 −
1989
100
 × 1 −
1989
100
 ×
3
100
 −
13923
10000
(1 +
3
100
) −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
12051
10000
 W − W ×
3
100
(1 +
17
100
) − W ×
21
10000
(1 +
17
100
) − W ×
9
10000
(1 +
17
100
) − W
    Remove a bracket on the right of the equation:：
     
1409967
10000
 −
1989
100
 × 1 −
1989
100
 ×
3
100
 −
13923
10000
(1 +
3
100
) −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
12051
10000
 W − W ×
3
100
 × 1 − W ×
3
100
 ×
17
100
 − W ×
21
10000
(1 +
17
100
) − W
    The equation is reduced to :
     
1409967
10000
 −
1989
100
 −
5967
10000
 −
13923
10000
(1 +
3
100
) −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
12051
10000
 W − W ×
3
100
 − W ×
51
10000
 − W ×
21
10000
(1 +
17
100
) − W ×
9
10000
(1 +
17
100
)
    The equation is reduced to :
     
12051
100
 −
13923
10000
(1 +
3
100
) −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
117
100
 W − W ×
21
10000
(1 +
17
100
) − W ×
9
10000
(1 +
17
100
) − W ×
3
5000
(1 +
17
100
)
    Remove a bracket on the left of the equation:
     
12051
100
 −
13923
10000
 × 1 −
13923
10000
 ×
3
100
 −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
117
100
 W − W ×
21
10000
(1 +
17
100
) − W ×
9
10000
(1 +
17
100
) − W ×
3
5000
(1 +
17
100
)
    Remove a bracket on the right of the equation:：
     
12051
100
 −
13923
10000
 × 1 −
13923
10000
 ×
3
100
 −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
117
100
 W − W ×
21
10000
 × 1 − W ×
21
10000
 ×
17
100
 − W ×
9
10000
(1 +
17
100
) − W
    The equation is reduced to :
     
12051
100
 −
13923
10000
 −
41769
1000000
 −
5967
10000
(1 +
3
100
) −
1989
5000
(1 +
3
100
) =
117
100
 W − W ×
21
10000
 − W ×
357
1000000
 − W ×
9
10000
(1 +
17
100
) − W ×
3
5000
(1 +
17
100
)

    
        W≈101.263348 , keep 6 decimal places    
    There are 1 solution(s).

解一元一次方程的详细方法请参阅：《一元一次方程的解法》



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