SOLUTION: A class trip cost ₱6000. If there had been 10 more student, it would have cost each student ₱30 less.How many students took the trip?

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Question 1068262: A class trip cost ₱6000. If there had been 10 more student, it would have cost each student ₱30 less.How many students took the trip?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
p, number of students

Actual trip:
, the price for one student

If 10 more students, trip:
, this price hypothetical


The hypothetical price is 30 money units less per student.

Solve this for p, the number of actual students going on the trip.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A class trip cost ₱6000. If there had been 10 more student, it would have cost each student ₱30 less.How many students took the trip?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let "n" be the number of students in the "basic version".

Then the cost for one student is .


If there had been 10 more students, the cost for each would be .


The condition says:

 = .


It is your equation to find "n". To solve it, multiply both sides by n*(n+1). You will get

6000(n+10) = 6000*n + 30*n*(n+10),

Simplify

60000 = 30*n*(n+10),

2000 = n*(n+10).

The solution is obvious (for me): n = 40.


You can solve this quadratic equation by any method/way you want.

Answer. 40 students in the basic version.



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