A cinema has 100 seats.
Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are:
£10 for adults
50p for pensioners
10p for children

Question

A cinema has 100 seats.
Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are:
£10 for adults
50p for pensioners
10p for children

anonymous · Answer

What does p stand for?

nastech · Answer

100p=1pound right?

anonymous · Answer

I have no idea, I live in Canada :)

anonymous · Answer

yes

anonymous · Answer

@jiji501 p stands for pence, I guess it would be cents in canada.

nastech · Answer

lets represent the number of adults with x and the number of pensioners with p and the number of children with z. and then lets convert all the values given in pounds to pence

nastech · Answer

|dw:1348332097918:dw|

nastech · Answer

solve the 2 equations simultaneously

anonymous · Answer

who gave this a medal?

anonymous · Answer

@Nastech its a stimulations equation with three unknowns.

anonymous · Answer

I'm running a simulation with random values to solve the problem.

anonymous · Answer

oh yes because x has to be between 0 and 9

anonymous · Answer

because if the number of adults is 10, we reach the total, but do not fill all the seats.

nastech · Answer

we can make x=20p( 1 adult is equivalent to 20 pensioners)

nastech · Answer

21x+20z=2000
20050x+200z=200000
we can solve these simultaneously

anonymous · Answer

I have an explicit solution :-D
8 adults
27 pensioners
65 children
Medal me!

anonymous · Answer

Here is the code http://dpaste.com/804537/