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If a, b, and c are integers satisfying \(a + \frac 1b = \frac{22}{7}\), \(b + \frac 1c = 8\), and abc = 21, then find \(c + \frac 1a\). Express your answer as a common fraction.

 Oct 9, 2019
 #1
avatar+8918 
+2

If a, b, and c are integers satisfying , , and abc = 21, then find . Express your answer as a common fraction.

 

\(\{a,b,c\}\subset \{1,3,7\}\ |abc=21\)

laugh  !

Sorry. Assignment incorrectly written off.

crying

 Oct 9, 2019
edited by asinus  Oct 10, 2019
 #2
avatar+107011 
+3

We can solve this by inspection. Logic

 

If  abc  =  21     and    a + 1/b  =  22/7

 

Then this implies that

 

a + 1/b  =  3  + 1/7

 

Which implies that  a  = 3    and  b  = 7

 

So

 

abc  =21

 

(3)(7)(1)  = 21

 

So  c  = 1

 

And

 

c + 1/a  =    1   + 1/3

 

 

 

cool cool cool

 Oct 10, 2019

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