Question 1198341
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Rewrite the improper fraction 17/5 into its mixed number format.
17/5 = (15+2)/5
17/5 = (15/5)+(2/5)
17/5 = 3+(2/5)
17/5 = 3 & 2/5


'a' is the integer part, or whole part, of the mixed number.
Therefore a = 3.


c is the numerator of the fractional part when the fraction is fully reduced. 
We have c = 2.


Let's simplify the left hand side of the given equation.
{{{ a +  1/( b+2/c ) = 17/5  }}}


{{{ a +  1/( (bc)/c+2/c ) = 17/5  }}}


{{{ a +  1/( (bc+2)/c ) = 17/5  }}}


{{{ a +  c/(bc+2) = 17/5  }}}


Then plug in a = 3 and c = 2.
Also, let's replace the 17/5 with 3 + 2/5 we found earlier.
{{{ a +  c/(bc+2) = 17/5  }}}


{{{ 3 +  2/(b*2+2) = 17/5  }}}


{{{ 3 +  2/(2b+2) = 17/5  }}}


{{{ 3 +  2/(2b+2) = 3 + 2/5  }}}
It's clear that the fractional part {{{2/(2b+2)}}} must be equal to 2/5. 
Furthermore, the denominator {{{2b+2}}} must be 5.


We'll use this fact to find b.
{{{2/(2b+2) = 2/5}}}


{{{2b+2 = 5}}}


{{{2b = 5-2}}}


{{{2b = 3}}}


{{{b = 3/2}}}


{{{b = 1.5}}}


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Summary:
a = 3
b = 3/2 = 1.5
c = 2


{{{a*b*c = 3*1.5*2 = 9}}}


Answer: <font color=red>Choice A) 9</font>
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