SOLUTION: The field trip of MATHADATZ POWER club cost ₱6000.if there had been 10more students,it would have cost each student ₱30 less.How many students took the field trip?

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Question 1186002: The field trip of MATHADATZ POWER club cost ₱6000.if there had been 10more students,it would have cost each student ₱30 less.How many students took the field trip?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
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%2Fx.

The cost of trip for each single hypothetical participant is  6000%2F%28x%2B10%29.


The difference in costs is 30, which gives this equation

    6000%2Fx - 6000%2F%28x%2B10%29 = 30.     (1)


To solve it, first divide both sides by 30

    200%2Fx - 200%2F%28x%2B10%29 = 1.       (2)


Now guess the answer MENTALLY:  x = 40.


CHECK.  200%2F40 - 200%2F%2840%2B10%29 = 5 - 4 = 1.    ! Correct !


ANSWER.  40 students took the trip.

Solved.

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