SOLUTION: A group of students is On a sightseeing tour. The total fare is $120 . And this is to be shared equally among the students. If two more students join the tour each will pay $2 les

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Question 1108378: A group of students is On a sightseeing tour. The total fare is $120
. And this is to be shared equally among the students. If two more students join the tour each will pay $2 less.find the original number of students in the group
Answer by ikleyn(52791) About Me  (Show Source):
You can put this solution on YOUR website!
.
The condition says 

N*P = 120            (1)
(N+2)*(P-2) = 120    (2)


where N = the number of students, P = how much each of N students must pay.


Transform (2) in this way:

N*P + 2P - 2N - 4 = 120,

120 + 2(P-N) - 4 = 120,

2*(P-N) = 4  ====>  P-N = 2.


So, you have 

PN = 120, 
P-N = 2,


and you can easily (MENTALLY) get the answer  P = 12, N = 10.