SOLUTION: A party of students rented a motor boat, Bee, and shared the cost equally. If the number of students had been 5 less, they could have used a smaller boat costing only half as much

Question 1890: A party of students rented a motor boat, Bee, and shared the cost equally. If the number of students had been 5 less, they could have used a smaller boat costing only half as much as Bee and the expense to each would have been 50 cents less. If there had been 10 more students in the party, they would have required a larger boat costing 20 per cent more than Bee, but the expense to each would have been 30 cents less. How many students were there in the party?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
i am not sure if i can do this...is there some other piece of info you have not given us?
Let s = number of students on Bee
Let c = cost for a student on Bee
so, on Bee, the cost of the boat is sc
Now, with 5 less students, the cost of the boat per person is c-50 whilst the total cost, sc/2 = (c-50)(s-5) --eqn1
Also, with 10 more students, the cost of the boat per person is c-30 whilst the total cost, 1.2sc = (c-30)(s+10) --eqn2
eqn1 becomes sc = 2(c-50)(s-5)
eqn2 becomes sc = (5/6)(c-30)(s+10)
we can equate these two and then expand the brackets and simplify to give
(7/6)cs - (110/6)c - 75s + 750 = 0
but i cannot figure out what to do next, but i could be missing something obvious - just not sure.
cheers
Jon.
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