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Positive integers a, b, c are 1/a + 1/b + 1/c = 6/7.  What is a + b + c?

 Oct 28, 2019
 #1
avatar+435 
+3

Look at this similar problem for help with this one https://www.quora.com/If-1-a-1-b-1-c-1-then-what-is-the-value-of-a-b-and-c

 Oct 28, 2019
 #2
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+1

a          b         c
42         3        2
3          42       2
42         2        3
2          42       3
3          2        42
2          3        42
a + b + c =42 + 3 + 2 = 47

 Oct 28, 2019
 #3
avatar+104933 
+1

We can use the concept of Egyptian Fractions to solve this

 

6/7    divide  7/6  and take the ceiling of this result  =  2

 

Take the reciprocal of this  =   1/2

 

So 

 

6/7  =  1/2 +  remainder

 

6/7 - 1/2  =  remainder

 

12/14 - 7/14  =  

 

5/14  = remainder

 

divide 14/5  and take the ceiling of this  = 3

 

Take the reciprocal of this   =1/3

 

So

 

6/7  =  1/2  + 1/3  + remainder

 

6/7  =  5/6 + remainder

 

6/7 - 5/6  = remainder

 

36 / 42  - 35/42  = remainder

 

1/42  =  remainder

 

So

 

6/7  =  1/2  + 1/3  + 1/42

 

 

cool cool cool

 Oct 28, 2019

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