Question 1186002
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<pre>
Let x be the number of participants;

then the hypothetical number of participants is (x+10).


The cost of the trip for each single participant is  {{{6000/x}}}.

The cost of trip for each single hypothetical participant is  {{{6000/(x+10)}}}.


The difference in costs is 30, which gives this equation

    {{{6000/x}}} - {{{6000/(x+10)}}} = 30.     (1)


To solve it, first divide both sides by 30

    {{{200/x}}} - {{{200/(x+10)}}} = 1.       (2)


Now guess the answer MENTALLY:  x = 40.


<U>CHECK</U>.  {{{200/40}}} - {{{200/(40+10)}}} = 5 - 4 = 1.    ! Correct !


<U>ANSWER</U>.  40 students took the trip.
</pre>

Solved.


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Alternatively, &nbsp;you may reduce equation &nbsp;(2) &nbsp;to the standard form quadratic equation and then solve it formally.