There is much excitement in the Jolly Quizmaster, as the landlord has organised a bus trip to visit another pub in the next village. Later in the year the other pub will organise a reciprocal trip, and so both pubs will benefit.
The landlord told us that he had originally got 30 people signed up, and had booked a 30-seater coach for the journey. However demand had been so high that five more people wanted to go, and luckily the coach company had a 35-seater available. He had just finished his phone call changing the arrangements.
"Well, that's a stroke of luck" he said, "I've managed to change the booking, and it is only going to cost an extra £10."
We agreed that it was indeed lucky that the 35-seater was available, but the extra £10 was not so lucky.
"But no" he said, "The cost per head has dropped by £1. Everyone will be paying less money to go".
On this basis, how much is each passenger now going to have to pay?
If the original cost of the bus was x, then the original cost per person was x/30. Now the cost of the bus is x + 10 and each person has to pay (x + 10)/35.
We know that the new cost per head is £1 lower so
x/30 - 1 = (x + 10)/35
35(x - 30) = 30(x + 10)
35x - 1050 = 30x + 300
5x = 1350
x = 270
So the original cost of the bus was £270, the new cost must be £280, and £280 shared between 35 passengers is £8.