Question 1122763
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            I am trying to find more simple way to solve it . . . 



<pre>
From the condition, you have these two equations for two unknowns


a  +  c = 54        (1)                    (a = # of adults;  c = # of children)

{{{a/5}}} +  {{{c/6}}} = 10       (2)


Multiply eq(2) by 6 (both sides).  Keep eq(1) as is.  You will get


a   +   c = 54      (3)                  

{{{(6a)/5}}} +  {{{c}}} = 60      (4)


From eq(4) subtract eq(3)  (both sides).  You will get


{{{a/5}}} = 60-54 = 6  ====>  a = 6*5 = 30   ====>  c = 54 - 30 = 24.


Now we have this simple system


Boys + Girls = 24
Boys - Girls =  4.

---------------------------- Add the two equations. You will get

2*Boys = 24 + 4 = 28  ====>  Boys = {{{28/2}}} = 14.
</pre>

Solved.


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Surely, &nbsp;I could start from a single equation for the unknown &nbsp;"C" &nbsp;only, &nbsp;instead of using two equations for &nbsp;"A" &nbsp;and &nbsp;"C".


But the major idea is clear:  &nbsp;The most simple way is to solve the problem in two steps:


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;first determine the number of children - and then &nbsp;(or after that) &nbsp;determine the number of boys.