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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation (720000+5a)/(144000*a)*1/(0.0333+(144000a/(144000+a))+(1/60000)) = 0.3 .
    Question type: Equation
    Solution:Original question:
     (720000 + 5 a ) ÷ (144000 a ) × 1 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
3
10
     Multiply both sides of the equation by:(144000 a )
     (720000 + 5 a ) × 1 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
3
10
(144000 a )
    Remove a bracket on the left of the equation::
     720000 × 1 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 5 a × 1 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
3
10
(144000 a )
    Remove a bracket on the right of the equation::
     720000 × 1 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 5 a × 1 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
3
10
× 144000 a
    The equation is reduced to :
     720000 ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) = 43200 a
     Multiply both sides of the equation by:(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
     720000 + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) = 43200 a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
    Remove a bracket on the left of the equation:
     720000 + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) ×
333
10000
+ 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a )) + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) = 43200 a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
    Remove a bracket on the right of the equation::
     720000 + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) ×
333
10000
+ 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a )) + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) = 43200 a ×
333
10000
+ 43200 a (144000 a ÷ (144000 + a )) + 43200 a (1 ÷ 60000)
    The equation is reduced to :
     720000 +
333
2000
a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a )) + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (1 ÷ 60000) =
35964
25
a + 43200 a (144000 a ÷ (144000 + a )) + 43200 a (1 ÷ 60000)
     Multiply both sides of the equation by:(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
     720000(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
333
2000
a + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
35964
25
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 43200 a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 43200 a (1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
    Remove a bracket on the left of the equation:
     720000 ×
333
10000
+ 720000(144000 a ÷ (144000 + a )) + 720000(1 ÷ 60000) +
333
2000
a + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a )) =
35964
25
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 43200 a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 43200 a (1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
    Remove a bracket on the right of the equation::
     720000 ×
333
10000
+ 720000(144000 a ÷ (144000 + a )) + 720000(1 ÷ 60000) +
333
2000
a + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a )) =
35964
25
a ×
333
10000
+
35964
25
a (144000 a ÷ (144000 + a )) +
35964
25
a (1 ÷ 60000) + 43200 a (144000 a ÷ (144000 + a ))
    The equation is reduced to :
     23976 + 720000(144000 a ÷ (144000 + a )) + 720000(1 ÷ 60000) +
333
2000
a + 5 a ÷ (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) × (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
2994003
62500
a +
35964
25
a (144000 a ÷ (144000 + a )) +
35964
25
a (1 ÷ 60000) + 43200 a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
     Multiply both sides of the equation by:(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
     23976(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 720000(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 720000(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
333
2000
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 5 =
2994003
62500
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
35964
25
a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
35964
25
a (1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 43200
    Remove a bracket on the left of the equation:
     23976 ×
333
10000
+ 23976(144000 a ÷ (144000 + a )) + 23976(1 ÷ 60000) + 720000(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 720000(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
2994003
62500
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
35964
25
a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
35964
25
a (1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 43200
    Remove a bracket on the right of the equation::
     23976 ×
333
10000
+ 23976(144000 a ÷ (144000 + a )) + 23976(1 ÷ 60000) + 720000(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 720000(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
2994003
62500
a ×
333
10000
+
2994003
62500
a (144000 a ÷ (144000 + a )) +
2994003
62500
a (1 ÷ 60000) +
35964
25
a (144000 a ÷ (144000 + a ))
    The equation is reduced to :
     
998001
1250
+ 23976(144000 a ÷ (144000 + a )) + 23976(1 ÷ 60000) + 720000(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 720000(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
333
2000
=
997002999
625000000
a +
2994003
62500
a (144000 a ÷ (144000 + a )) +
2994003
62500
a (1 ÷ 60000) +
35964
25
a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
     Multiply both sides of the equation by:(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))
     
998001
1250
(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 23976(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 23976(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 720000(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
997002999
625000000
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
2994003
62500
a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
2994003
62500
a (1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
35964
25
    Remove a bracket on the left of the equation:
     
998001
1250
×
333
10000
+
998001
1250
(144000 a ÷ (144000 + a )) +
998001
1250
(1 ÷ 60000) + 23976(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 23976(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
997002999
625000000
a (
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
2994003
62500
a (144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
2994003
62500
a (1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) +
35964
25
    Remove a bracket on the right of the equation::
     
998001
1250
×
333
10000
+
998001
1250
(144000 a ÷ (144000 + a )) +
998001
1250
(1 ÷ 60000) + 23976(144000 a ÷ (144000 + a ))(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) + 23976(1 ÷ 60000)(
333
10000
+ (144000 a ÷ (144000 + a )) + (1 ÷ 60000)) =
997002999
625000000
a ×
333
10000
+
997002999
625000000
a (144000 a ÷ (144000 + a )) +
997002999
625000000
a (1 ÷ 60000) +
2994003
62500
a (144000 a ÷ (144000 + a ))
    
    There are 0 solution(s).


解程的详细方法请参阅:《方程的解法》



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