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) About Me  (Show Source):
You can put this solution on YOUR website!
p, number of students

Actual trip:
6000%2Fp, the price for one student

If 10 more students, trip:
6000%2F%28p%2B10%29, this price hypothetical


The hypothetical price is 30 money units less per student.
highlight%286000%2Fp-6000%2F%28p%2B10%29=30%29
Solve this for p, the number of actual students going on the trip.

Answer by ikleyn(52786) About Me  (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?
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Let "n" be the number of students in the "basic version".

Then the cost for one student is 6000%2Fn.


If there had been 10 more students, the cost for each would be 6000%2F%28n%2B10%29.


The condition says:

6000%2Fn = 6000%2F%28n%2B10%29+%2B+30.


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.