Question 1201935
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For positive numbers a, b, and c, if 2ab = 1, 3bc = 2, and 4ca = 3, what is the value of a + b + c ?
(A) 29/12
(B) 9/4
(C) 25/12
(D) 23/12
(E) 7/4
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        The solution by @math_tutor is correct,  but can make you shudder.


        I will show you an elegant,  simple and fine  STANDARD  solution to this 

        and similar problems,  which will make you more than happy.



<pre>
From the given info, we have these equations

    ab = {{{1/2}}}     (1)

    bc = {{{2/3}}}     (2)

    ac = {{{3/4}}}     (3)


Multiply all these three equations (their left sides and their right sides separately).  You will get

    a^2*b^2*c^2 = {{{(1/2)*(2/3)*(3/4)}}} = {{{1/4}}},

or

    (a*b*c)^2 = {{{1/4}}}.


Take the square root of both sides.  Since "a", "b", and "c" are positive, it gives you

    a*b*c = {{{1/2}}}.   (4)


At this point, you may find "a", "b" and "c" separately.

    To find "a", divide (4) by (2);

    To find "b", divide (4) by (3);

    To find "c", divide (4) by (1).


You will get  a = {{{((1/2))/((2/3))}}} = {{{3/4}}};  b = {{{((1/2))/((3/4))}}} = {{{2/3}}};  c = {{{((1/2))/((1/2))}}} = 1.

Now a + b + c = {{{3/4}}} + {{{2/3}}} + 1 = {{{9/12}}} + {{{8/12}}} + {{{1}}} = {{{17/12}}} + {{{1}}} = {{{29/12}}}.    <U>ANSWER</U>
</pre>

Solved.


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Memorize this method and use it for other similar problems.