Question 670058
<pre>
Let the total number of students = N
</pre>
>>...2/5 of the students are taking chemistry,...<<
<pre>
So {{{2/5}}}N are taking chemistry
</pre>
 1/3 of the remaining students are taking physics,
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The trick here is "the remaining students".  That is NOT 
{{{1/3}}} of the total number of students!  It is only
{{{1/3}}} of the students that remain after the {{{2/5}}}N
chemistry students have been subtracted from N, which is 
N - {{{2/5}}}N or {{{3/5}}}N.  Therefore {{{1/3}}} of {{{3/5}}}N 
is {{{1/5}}}N.  So the number talking physics is {{{1/5}}}N.

and the rest are taking biology. 

"The rest" is found by subtracting the {{{2/5}}}N taking
chemistry and the {{{1/5}}}N taking physics from N:

N - ({{{2/5}}}N + {{{1/5}}}N) = N - {{{3/5}}}N = {{{2/5)))N

so {{{2/5}}}N are taking biology 
</pre>
>>...66 students are taking biology,...<<
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So we set {{{2/5)))N equal to 66. 

{{{2/5}}}N = 66

Multiply through by 5

2N = 330
 N = 165

Edwin</pre>