SOLUTION: A group of students is on a sightseeing tour. The total fare is $120 and this is to be shared equally among students.if two more students join the tour, each will pay $2 less. Find

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Question 901205: A group of students is on a sightseeing tour. The total fare is $120 and this is to be shared equally among students.if two more students join the tour, each will pay $2 less. Find the original number of students in the group.
Found 2 solutions by JulietG, josgarithmetic:
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
I did this through trial and error, and hit on the first guess. I simply took the factors of 120 and assumed they would be the ones closest together {10,12}. If you need a strictly mathematical approach, please repost.

Original number of students = 10
Each then pays $12
Add two students to get 12
Each then pays $10

ETA: Awesome explanation, JogsArithmetic.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x = original number of students
trip cost, 120 dollars.
Student's price = 120%2Fx.

If x+2 students, then 2 dollars per student less.
120%2F%28x%2B2%29=120%2Fx-2.
The left member is the price if two more students, and the right member is original student price minus $2.
They are described as equal.

SOLUTION ARITHMETIC STEPS
LCD is x%28x%2B2%29.
120x=120%28x%2B2%29-2%28x%28x%2B2%29%29
120x=120x%2B240-2x%5E2-4x
0=240-2x%5E2-4x
2x%5E2%2B4x-240=0
x%5E2%2B2x-120=0
highlight_green%28%28x-10%29%28x%2B12%29=0%29
highlight%28x=10%29 students, original number.
cross%28x=-12%29