Question 1205847
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Chairs are arranged in the hall into 18 short rows and 7 long rows. 
Each long row has 18 more chairs than each short row. 
1/2 of the chairs are arranged into long rows. 
3/7 of the chairs are arranged into short rows. 
The remaining chairs are stacked in a corner.
(a) What fraction of the chairs are stacked in the corner?
(b) How many chairs are arranged in long rows?
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        I use different setup comparing with that of @greenestamps.



<pre>
(a)  The answer for question (a) is simple arithmetic

         1 - {{{1/2}}} - {{{3/7}}} = write with common denominator of 14 = 1 - {{{7/14}}} - {{{6/14}}} = 1 - {{{13/14}}} = {{{1/14}}}.

     We will use this value 1/14 in part (b).



(b)  Part (b) is more interesting. Its setup is quite unusual.


     Let x be the number of chairs in each long row.

     Then the number of rows in short rows is (x-18), according to the problem.


     The number of rows in all 7 long rows is 7x.

     The number of chairs in all 18 short rows is 18*(x-18).


     Since 1/2 of the chairs are arranged into long rows, the total number of chairs is twice 7x, or 14x.
     Hence, the other half is 7x, and it consists of 18*(x-18) chairs in short rows AND 1/14 of the total chairs, 14x, in the corner.


     Based on it, we can write this equation for the second half

         7x = 18*(x-18) + {{{(1/14)*14x}}}.


     The setup is complete. Now simplify the last equation and find x

         7x = 18x - 324 + x

         324 = 18 + x - 7x

         324 = 12x

           x = 324/12 = 27.


     Thus we get for (b) 27 chairs in each long row and 27*7 = 189 chairs in all 7 long chairs, altogether.
</pre>

Solved.