SOLUTION: URGENT HELP. The student council of XYZ School needed P225,000 for an annual trip. If five more members joined the group, each member would then save P500. How many students plan

Question 998781: URGENT HELP. The student council of XYZ School needed P225,000 for an annual trip. If five more members joined the group, each member would then save P500. How many students planned to make the trip?
Thank you :)

Found 2 solutions by mananth, KMST:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let the number of students initially be x
so cost per student = 225,000/x
5 more joined
cost per student = 225,000/(x+5)
difference is 500
225000/x - 225000/(x+5) =500
multiply by x(x+5)
225000(x+5) -225000x= 500(x)(x+5)
225000x+1125000-225000x = 500x^2+2500x
500x^2+2500x-1125000=0
/500
x^2+5x-2250=0
x^2+50x-45x-2259=0
x(x+50) -45(x+50)=0
(x+50)(x-45)=0
x = -50 or 45
discard -50
answer 45 students initially
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
So , hiring the transportation for the ,
and the cost per student is .
However, since they have some free seats on the hired transportation,
they could transport more students for the same total cost.
Then, the cost per student would be .
If that is less, that means that

Multiplying both sides of the equal sign times (which is not zero),
we get the equivalent equation

Now, you have to solve that equation.
You could see that it is a quadratic equation,
you could re-write it in a more traditional form,
as ,
and solve it whichever way will make your teacher satisfied
(factoring, completing the square, or using the quadratic formula).
Alternatively, from ,
you could look for factors and whose product is ,
and finding that ,
you would conclude that .
So students planned to make the trip.
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