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    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation Y = 1+Y/(1+13%)×13%+[Y/(1+13%)×13%-1×1%]×（7%+3%+2%） .
    Question type: Equation
    Solution:Original question:
      Y = 1 + Y ÷ (1 +
13
100
) ×
13
100
 + ( Y ÷ (1 +
13
100
) ×
13
100
 − 1 ×
1
100
)(
7
100
 +
3
100
 +
2
100
)
     Multiply both sides of the equation by:(1 +
13
100
)
      Y (1 +
13
100
) = 1(1 +
13
100
) + Y ×
13
100
 + ( Y ÷ (1 +
13
100
) ×
13
100
 − 1 ×
1
100
)(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    Remove a bracket on the left of the equation:：
      Y × 1 + Y ×
13
100
 = 1(1 +
13
100
) + Y ×
13
100
 + ( Y ÷ (1 +
13
100
) ×
13
100
 − 1 ×
1
100
)(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    Remove a bracket on the right of the equation:：
      Y × 1 + Y ×
13
100
 = 1 × 1 + 1 ×
13
100
 + Y ×
13
100
 + ( Y ÷ (1 +
13
100
) ×
13
100
 − 1 ×
1
100
)(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    The equation is reduced to :
      Y × 1 + Y ×
13
100
 = 1 +
13
100
 + Y ×
13
100
 + ( Y ÷ (1 +
13
100
) ×
13
100
 − 1 ×
1
100
)(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    The equation is reduced to :
     
113
100
 Y =
113
100
 +
13
100
 Y + ( Y ÷ (1 +
13
100
) ×
13
100
 − 1 ×
1
100
)(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    Remove a bracket on the right of the equation:：
     
113
100
 Y =
113
100
 +
13
100
 Y + Y ÷ (1 +
13
100
) ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) − 1 ×
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    The equation is reduced to :
     
113
100
 Y =
113
100
 +
13
100
 Y + Y ÷ (1 +
13
100
) ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
     Multiply both sides of the equation by:(1 +
13
100
)
     
113
100
 Y (1 +
13
100
) =
113
100
(1 +
13
100
) +
13
100
 Y (1 +
13
100
) + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    Remove a bracket on the left of the equation:
     
113
100
 Y × 1 +
113
100
 Y ×
13
100
 =
113
100
(1 +
13
100
) +
13
100
 Y (1 +
13
100
) + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    Remove a bracket on the right of the equation:：
     
113
100
 Y × 1 +
113
100
 Y ×
13
100
 =
113
100
 × 1 +
113
100
 ×
13
100
 +
13
100
 Y (1 +
13
100
) + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
    The equation is reduced to :
     
113
100
 Y +
1469
10000
 Y =
113
100
 +
1469
10000
 +
13
100
 Y (1 +
13
100
) + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
13
100
 Y (1 +
13
100
) + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)(1 +
13
100
)
    Remove a bracket on the right of the equation:：
     
12769
10000
 Y =
12769
10000
 +
13
100
 Y × 1 +
13
100
 Y ×
13
100
 + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
13
100
 Y +
169
10000
 Y + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
1469
10000
 Y + Y ×
13
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)(1 +
13
100
)
    Remove a bracket on the right of the equation:：
     
12769
10000
 Y =
12769
10000
 +
1469
10000
 Y + Y ×
13
100
 ×
7
100
(1 +
13
100
) + Y ×
13
100
 ×
3
100
(1 +
13
100
) + Y
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
1469
10000
 Y + Y ×
91
10000
(1 +
13
100
) + Y ×
39
10000
(1 +
13
100
) + Y ×
13
5000
(1 +
13
100
)
    Remove a bracket on the right of the equation:：
     
12769
10000
 Y =
12769
10000
 +
1469
10000
 Y + Y ×
91
10000
 × 1 + Y ×
91
10000
 ×
13
100
 + Y ×
39
10000
(1 +
13
100
)
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
1469
10000
 Y + Y ×
91
10000
 + Y ×
1183
1000000
 + Y ×
39
10000
(1 +
13
100
) + Y ×
13
5000
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
157183
1000000
 Y + Y ×
39
10000
(1 +
13
100
) + Y ×
13
5000
(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)
    Remove a bracket on the right of the equation:：
     
12769
10000
 Y =
12769
10000
 +
157183
1000000
 Y + Y ×
39
10000
 × 1 + Y ×
39
10000
 ×
13
100
 + Y ×
13
5000
(1 +
13
100
)
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
157183
1000000
 Y + Y ×
39
10000
 + Y ×
507
1000000
 + Y ×
13
5000
(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)
    The equation is reduced to :
     
12769
10000
 Y =
12769
10000
 +
16159
100000
 Y + Y ×
13
5000
(1 +
13
100
) −
1
100
(
7
100
 +
3
100
 +
2
100
)(1 +
13
100
)(1 +
13
100
)

    
        Y≈0.896825 , 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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