SOLUTION: If {{{ 45/7=a+(1/c)/(1/b) }}}, where a, b, and c are positive integers, and b < c, evaluate the value of abc.

Algebra ->  Expressions-with-variables -> SOLUTION: If {{{ 45/7=a+(1/c)/(1/b) }}}, where a, b, and c are positive integers, and b < c, evaluate the value of abc.      Log On


   

Question 1105717: If +45%2F7=a%2B%281%2Fc%29%2F%281%2Fb%29+, where a, b, and c are positive integers, and b < c, evaluate the value of abc.
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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If +45%2F7=a%2B%281%2Fc%29%2F%281%2Fb%29+, where a, b, and c are positive integers, and b < c, evaluate the value of abc.
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45%2F7 = 6 + 3%2F7 = a + %281%2Fc%29%2F%281%2Fb%29 = a + b%2Fc.


Since "b" and "c" are positive integers with b < c, you can conclude that b%2Fc < 1.

Hence,  a = 6.


But for "b" and "c" you have INFINITELY MANY answers (b,c) = (3,7),  (6,14),  (9,21) . . . and so on . . . 


Therefore, IT IS NOT POSSIBLE to evaluate the value of abc by an UNIQUE way.


Your problem is posed INCORRECTLY.